drimmR : R Package for Estimation, Simulation and Reliability of drifting Markov Models • drimmR

Introduction

In this work we focus on multi-state systems modeled by means of a particular class of non-homogeneous Markov processes introduced in Vergne (2008), called drifting Markov processes. Most of the estimation methods and reliability results are developed in Barbu and Vergne (2019).

Note that in many mathematical models it is assumed the homogeneity with respect to time, which is inappropriate in most of the applications. But, considering general non-homogeneous processes could be unrealistic from a practical point of view. For this reason, the drifting Markov chains assume that the Markov transition matrix is a linear/polynomial function of two/several Markov transition matrices. Thus we obtain a “smooth” non-homogeneity, with sensibly less parameters than in the general case.

Few R packages have been developed to handle similar types of models of Markov, semi-Markov or hidden semi-Markov type, useful in reliability or DNA analysis. For semi-Markov models we have semiMarkov R package Król and Saint-Pierre (2015) that performs maximum likelihood estimation for parametric continuous-time semi-Markov processes, smm R package Barbu, Bérard, et al. (2018) which performs parametric and non-parametric estimation and simulation for multi-state discrete-time semi-Markov processes. Two R packages are also dedicated to hidden semi-Markov models, implementing estimation and prediction methods: the hsmm R package Bulla, Bulla, and Nenadić (2010) and the mhsmm R package O’Connell and Højsgaard (2011).

Note that there is no R package developed for drifting Markov models (DMMs). Thus the purpose of this paper is to present an R package that we have developed, called drimmR, which performs estimation and simulation for such models, as well as the estimation of associated reliability measures. The aim of this paper is to describe the different possibilities of this package. To summarize, the package drimmR that we present deals with different problems:

We consider one or several sample paths; for several sample paths, two estimation methods are proposed: one is the usual LSE, the other one is the average of LSEs obtained on each sample;
The samples paths are complete or incomplete;
The sample paths come from drifting Markov chains that are of the same length or of different lengths (between the same Markov transition probability matrices);
We derive exact computations of reliability/survival analysis measures (reliability or survival function, availability, maintainability, failure rates);
We compute the probabilities of appearance of a word in a given sequence under a given model.

We would like to mention that a web interface called WebDRIMM has been also developed [cf. Barbu, Brelurut, et al. (2018)] for simulating and estimating drifting Markov models, as well as associated reliability indicators; it is available at http://bioinfo.univ-rouen.fr/WebDRIMM
The paper is organized as follows. Section 2 describes the drifting Markov models used in this package, present associated reliability indicators and corresponding estimation results and techniques. Section 3 illustrates the different functions of the drimmR package and we end the paper by presenting some concluding remarks on this R package in Section 4.

Drifting Markov models, estimation and associated reliability measures

Let us consider a random system with finite state space $E=\{1,\ldots, s\}$ , $s < \infty.$ We assume that the time evolution of a system is governed by a discrete-time stochastic process with values in $E.$ In the following we will introduce a class of processes according to Vergne (2008) in Section 2.1, we will briefly present associated reliability indicators according to Barbu and Vergne (2019) in Section 2.2 and estimation of the parameters in Section 2.3, according to Vergne (2008) Barbu and Vergne (2019).

Drifting Markov models

Let $\boldsymbol{\Pi}_0 = (\Pi_0(u, v))_{u,v \in E}$ and $\boldsymbol{\Pi}_1 = (\Pi_1(u, v))_{u,v \in E}$ be two Markov transition matrices of order 1 over the state space $E.$

Definition 1 (linear drifting Markov chain of order $1$ and of length $n$ ). A sequence $X_0,$ $X_1, \ldots, X_n$ with state space $E=\mathbb \{1, 2, \ldots, s\}$ is said to be a linear drifting Markov chain (of order 1)* of length $n$ between the Markov transition matrices $\boldsymbol{\Pi}_0$ and $\boldsymbol{\Pi}_1$ if the distribution of $X_t,$ $t = 1, \ldots, n,$ is defined by $\label{eq_DriftLin1} \mathbb P(X_t=v \mid X_{t-1} = u, X_{t-2}, \ldots ) = \Pi_{\frac{t}{n}}(u, v), \; u, v \in E,$ where $\label{eq_DriftLin2} \Pi_{\frac{t}{n}}(u, v) = \left( 1 - \frac{t}{n} \right) \Pi_0(u, v) + \frac{t}{n} \Pi_1(u, v), \; u, v \in E.$ *

Let us denote by $\boldsymbol{\alpha} = (\alpha(1), \ldots, \alpha(s))$ the initial distribution of the chain, that is the distribution of $X_0,$ $\alpha(u)=\mathbb P (X_0 = u)$ for any state $u\in E.$

The linear drifting Markov model of order $1$ can be generalized to polynomial drifting Markov model of order $k$ and degree $d$ . Let $\boldsymbol{\Pi}_{\frac{i}{d}} = (\boldsymbol{\Pi}_{\frac{i}{d}}(u_1, \dots, u_k, v))_{u_1, \dots, u_k,v \in E}$ be $d$ Markov transition matrices (of order $k$ ) over a state space $E.$

Definition 2 (polynomial drifting Markov chain of order $k$ and of length $n$ ). A sequence $X_0,$ $X_1,$ $\ldots,$ $X_n$ with state space $E=\mathbb \{1, 2, \ldots, s\}$ is said to be a polynomial drifting Markov chain of order k* and of length $n$ if the distribution of $X_t,$ $t = 1, \ldots, n,$ is defined by $\label{eq_DriftPol1} \mathbb P(X_t=v \mid X_{t-1} = u_k, X_{t-2}=u_{k-1}, \ldots ) = \boldsymbol{\Pi}_{\frac{t}{n}}(u_1, \dots, u_k, v), \; u_1, \dots, u_k, v \in E,$ where $\label{eq_DriftPol2} \boldsymbol{\Pi}_{\frac{t}{n}}(u_1, \dots, u_k, v) = \displaystyle\sum_{i=0}^d A_i(t)\boldsymbol{\Pi}_{\frac{i}{d}}(u_1, \dots, u_k,v), \; u_1, \dots, u_k, v \in E,$ with $A_i$ polynomials of degree $d$ such as, for any $i, j \in \{0, 1, \ldots, d\},$ $A_i\left(\frac{nj}{d}\right)=\mathbb{1}_{\{i=j\}}.$ *

We would like to stress that the coherence between notations implies the choice of the notation $\boldsymbol{\Pi}_{\frac{i}{d}}$ and that, in fact, $A_i$ are Lagrange polynomials; see Vergne (2008) for more details on these two points.

Reliability of drifting Markov models

In order to undertake a reliability analysis of a system modeled by a DMM, let us assume that the state space of the system is partitioned into working and failure states, $E=U \cup D,$ with $U \cap D=\emptyset,$ where $U=\{1,\ldots,s_1\}$ represents the working states and $D=\{s_1+1,\ldots,s\}$ the failure states of the system. According to this partition of the state space we partition any matrix of vector we are working with and we denote the corresponding partitions accordingly (e.g., $\boldsymbol{\Pi}_0^{UU},$ $\boldsymbol{\Pi}_0^{DU},$ $\boldsymbol{\alpha}^{U}$ etc.).

For a linear drifting Markov chain of order $1$ $(X_t)_{0 \leq t \leq n},$ the reliability at time $l,$ $l \in \mathbb N,$ is given by $\label{eq_RelDrift} R(l) = \boldsymbol{\alpha}^{U} \; \prod_{t=1}^l \left( \left(1 - \frac{t}{n}\right) \boldsymbol{\Pi}_0^{UU} + \frac{t}{n} \boldsymbol{\Pi}_1^{UU} \right) \; \mathbb{1}^U, \textrm{ where } \mathbb{1}^U = (\underbrace{1, \cdots, 1}_{s_1})^{\top}.$

For a linear drifting Markov chain of order $1$ $(X_t)_{0 \leq t \leq n},$ the pointwise (or instantaneous) availability at time $l,$ $l \in \mathbb N,$ is given by $\label{eq_AvDrift} A(l) = \boldsymbol{\alpha} \; \prod_{t=1}^l \left( \left(1 - \frac{t}{n}\right) \boldsymbol{\Pi}_0 + \frac{t}{n} \boldsymbol{\Pi}_1 \right) \; \mathbb{1}^{E,U}, \textrm{ where } \mathbb{1}^{E,U} = (\underbrace{1, \cdots, 1}_{s_1}, \underbrace{0, \cdots, 0}_{s-s_1} )^{\top}.$

For a linear drifting Markov chain of order $1$ $(X_t)_{0 \leq t \leq n},$ the maintainability at time $l,$ $l \in \mathbb N,$ is given by $\label{eq_MaintDrift_gen} M(l) = 1 - \boldsymbol{\alpha}^{D} \; \prod_{t=1}^l \left( \left(1 - \frac{t}{n}\right) \boldsymbol{\Pi}_0^{DD} + \frac{t}{n} \boldsymbol{\Pi}_1^{DD} \right) \; \mathbb{1}^D, \textrm{ where } \mathbb{1}^D = (\underbrace{1, \cdots, 1}_{s-s_1})^{\top}.$

For a linear drifting Markov chain of order $1$ $(X_t)_{0 \leq t \leq n},$ the BMP-failure rate at time $l at time$ l,$ $l N,$ is given by % $\begin{equation} \label{eq_BMPDrift} \lambda(l) \left\{ \begin{array}{ll} 1- \frac{\mu_0^U \ \prod_{t=1}^{l}( \ (1-\frac{t}{n}) \pi_0^{UU} + (\frac{t}{n}) \pi_1^{UU}) \ \mathbb{1}^U}{\mu_0^U \ \prod_{t=1}^{l-1}( \ (1-\frac{t}{n}) \pi_0^{UU} + (\frac{t}{n}) \pi_1^{UU}) \ \mathbb{1}^U} \ \ , \ \text{si R(l-1) != 0 }\\ 0 \ , \ otherwise \\ \end{array} \right. \end{equation}$

\end{proposition}

\begin{proposition} For a linear drifting Markov chain of order $1$ $(X_t)\_0t n,$ the RG-failure rate at time$l at time $l,$ $l \in \mathbb N,$ is given by $\label{eq_RGDrift} r(l) \left\{ \begin{array}{ll} -\ln \frac{\mu_0^U \ \prod_{t=1}^{l}( \ (1-\frac{t}{n}) \pi_0^{UU} + (\frac{t}{n}) \pi_1^{UU}) \ \mathbb{1}^U}{\mu_0^U \ \prod_{t=1}^{l-1}( \ (1-\frac{t}{n}) \pi_0^{UU} + (\frac{t}{n}) \pi_1^{UU}) \ \mathbb{1}^U} \ \ , \ if \ l \ge 1 \ ,\\ -\ln R(0) \ , \ if \ \ l = 0 \\ \end{array} \right.$

See Barbu and Vergne (2019) for more details and Barbu and Limnios (2004); Barbu and Limnios (2008) for similar questions in a discrete-time semi-Markov framework.

Estimation of drifting Markov models

In this section we will consider different types of data for which the estimators of the characteristics of a drifting Markov chain and of the associated reliability indicators will be derived.

One can observe one sample path, that will be denoted by ${\mathcal H}(m,n):= (X_0,X_1, \ldots,X_{m}),$ where $m$ denotes the length of the sample path and $n$ the length of the drifting Markov chain. Two cases can be considered: (a1) $m=n$ (a complete sample path); (a2) $m < n$ (an incomplete sample path).

One can also observe $H$ i.i.d. sample paths, ${\mathcal H}_i(m_i,n_i), i=1, \ldots, H.$ Four cases can be considered here: (b1) $m_i=n_i=n$ for all $i=1, \ldots, H$ (complete sample paths of drifting Markov chains of the same length) ; (b2) $n_i=n$ for all $i=1, \ldots, H$ (incomplete sample paths of drifting Markov chains of the same length); (b3) $m_i=n_i$ for all $i=1, \ldots, H$ (complete sample paths of drifting Markov chains of different lengths) ; (b4) $m_i \leq n_i$ for all $i=1, \ldots, H$ (incomplete sample paths of drifting Markov chains of different lengths).

We have developed cf. Vergne (2008); Barbu and Vergne (2019) mean square estimators starting from data under these frameworks; we present here only the case of a linear drifting Markov chain of order $1$ under the sample framework (b1) (complete sample paths of drifting Markov chains of the same length).

Under the setting (b1), starting with $H$ complete sample paths of drifting Markov chains of the same length of a linear drifting Markov chain between two Markov transition matrices (of order 1) $\boldsymbol{\Pi}_0$ and $\boldsymbol{\Pi}_1,$ for any states $u, v \in E,$ the estimators of $\Pi_0(u,v)$ and $\Pi_1(u,v)$ are given by:

$\begin{aligned} &&\widehat{\Pi}_{0; (n,H)} (u,v) = \frac{P_1(H, \boldsymbol{m}, \boldsymbol{n}) P_2(H, \boldsymbol{m}, \boldsymbol{n}) - P_3(H, \boldsymbol{m}, \boldsymbol{n})P_4(H, \boldsymbol{m}, \boldsymbol{n})} {P_5(H, \boldsymbol{m}, \boldsymbol{n}) P_1(H, \boldsymbol{m}, \boldsymbol{n}) - P_3(H, \boldsymbol{m}, \boldsymbol{n})^2}\\ && \widehat{\Pi}_{1; (n,H)} (u,v)=\frac{P_5(H, \boldsymbol{m}, \boldsymbol{n}) P_4(H, \boldsymbol{m}, \boldsymbol{n}) - P_3(H, \boldsymbol{m}, \boldsymbol{n}) P_2(H, \boldsymbol{m}, \boldsymbol{n})} {P_5(H, \boldsymbol{m}, \boldsymbol{n})P_1(H, \boldsymbol{m}, \boldsymbol{n}) - P_3(H, \boldsymbol{m}, \boldsymbol{n})^2},\end{aligned}$

where we have introduced the following notation:

$\displaystyle P_1(H, \boldsymbol{m}, \boldsymbol{n}) = \sum_{t=1}^{m}\sum_{h=1}^H \mathbb{1}_{\{X_{t-1}^h=u \}} \left(\frac{t}{n}\right)^2,$ $\displaystyle P_2(H, \boldsymbol{m}, \boldsymbol{n}) = \sum_{t=1}^{m} \sum_{h=1}^H\mathbb{1}_{\{X_{t-1}^h=u, X_t^h=v \}} \left(1-\frac{t}{n}\right),$
$\displaystyle P_3(H, \boldsymbol{m}, \boldsymbol{n}) = \sum_{t=1}^{m}\sum_{h=1}^H\mathbb{1}_{\{X_{t-1}^h=u \}} \left(1-\frac{t}{n}\right)\left(\frac{t}{n}\right),$ $\displaystyle P_4(H, \boldsymbol{m}, \boldsymbol{n}) = \sum_{t=1}^{m}\sum_{h=1}^H\mathbb{1}_{\{X_{t-1}^h=u, X_t^h=v \}}\left(\frac{t}{n}\right),$
$\displaystyle P_5(H, \boldsymbol{m}, \boldsymbol{n}) = \displaystyle\sum_{t=1}^{m}\sum_{h=1}^H\mathbb{1}_{\{X_{t-1}^h=u \}}\left(1-\frac{t}{n}\right)^2,$ with $\boldsymbol{m}=(m_1, \ldots, m_H)$ and $\boldsymbol{n}=(n_1, \ldots, n_H).$

Note we can adapt the estimation procedures that we have previously obtained in order to get estimators of the drifting Markov models in the other cases; one can see Barbu and Vergne (2019) for more details. Using the expression of the reliability indicators of a drifting Markov chain previously obtained and the estimators of the characteristics of a drifting Markov chain, one immediately obtains the associated plug-in estimators of the reliability metrics.

The package

The package is principally devoted to the simulation and estimation of drifting Markov models, as well as to the estimation of associated reliability measures and to the computation of the probabilities of a word occurrence under a given model. All the different possibilities of the package are illustrated in Figure 2.

Estimation of drifting Markov models

The estimation of DMMs is carried out by the functions fitdmm, when starting from one (several) sample path (and obtain LSE). We will describe this function in the sequel.

The function fitdmm

The different arguments of this function are:

sequences: A list of character vector(s) representing one (several) sequence(s) from which the estimation is carried out
order: Order of the Markov chain
degree: Degree of the polynomials (e.g., linear drifting if degree=1, etc.)
states: Vector of states space of length s > 1
init.estim: Method used to estimate the initial law.

Here we have an example of an estimation of a drifting Markov model of order 1 and degree 1 using the function fitdmm, starting from a DNA sequence called lambda.

data(lambda, package = "drimmR")
states <- c("a","c","g","t")
dmm <- fitdmm(lambda, 1, 1, states, init.estim="freq", fit.method="sum")
dmm
## $states
## [1] "a" "c" "g" "t"
## 
## $order
## [1] 1
## 
## $degree
## [1] 1
## 
## $Polynomials
##     t^0 t^1
## A_0   1  -1
## A_1   0   1
## 
## $length
## [1] 48501
## 
## $matrices
## $matrices$Pi0
##           a         c         g         t
## a 0.2548330 0.2495270 0.2593907 0.2362493
## c 0.2353305 0.2465529 0.3360221 0.1820945
## g 0.2313610 0.3008693 0.2879023 0.1798674
## t 0.1356776 0.2174431 0.4129533 0.2339260
## 
## $matrices$Pi1
##           a         c         g         t
## a 0.3398007 0.1715523 0.1870335 0.3016135
## c 0.3339285 0.1911412 0.2075945 0.2673358
## g 0.2801369 0.2600487 0.2021395 0.2576749
## t 0.2218131 0.2283645 0.2305177 0.3193047
## 
## 
## $init.estim
## 
##         a         c         g         t 
## 0.2543400 0.2342171 0.2642778 0.2471651 
## 
## attr(,"class")
## [1] "dmm"

Estimation of corresponding model characteristics

Once a Markov drifting model has been estimated/constructed as described in the previous subsection, various characteristics of the model can be computed. These are: the log-likelihood of one or several sequences, the AIC and BIC information criteria, the stationary distribution on an entire sequence or only on a part of it, the distribution of the chain on the entire sequence or only on a part of it.

The functions loglik, aic and bic have the following arguments:

x: Object of class dmm
sequences: A list of character vector(s) representing one (several) sequence(s)

They return the numerical values of the log-likelihood, the AIC, the BIC of the sequence, respectively.

data(lambda, package = "drimmR")
sequence <- c("a","g","g","t","c","g","a","t","a","a","a")
dmm <-fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq")

loglik(dmm, sequence)
## [[1]]
## [1] -16.08786

aic(dmm, sequence)
## [[1]]
## [1] 80.17572

bic(dmm, sequence)
## [[1]]
## [1] 89.72521

The function getTransitionMatrix evaluates the transition matrix at a given position. The function has the following arguments :

x: Object of class dmm
pos: position along the sequence (integer)

data(lambda)
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'),init.estim = "freq")
t <- 10
getTransitionMatrix(dmm,pos=t)
##           a         c         g         t
## a 0.2548505 0.2495109 0.2593757 0.2362628
## c 0.2353509 0.2465415 0.3359956 0.1821121
## g 0.2313710 0.3008609 0.2878846 0.1798834
## t 0.1356954 0.2174453 0.4129157 0.2339436

The function getStationaryLaw evaluates the stationary law at a given position or for all positions along the list of sequence(s).

x: Object of class dmm
pos: position along the sequence (integer)
all.pos: FALSE (default, evaluation at pos index) ; TRUE (evaluation for all pos index)
internal: FALSE (default) ; TRUE (for internal use of fitdmm initial law)

data(lambda, package = "drimmR")
sequence <- sample(lambda, 30, replace=TRUE )
dmm <- fitdmm(sequence, 1, 1, c('a','c','g','t'), init.estim = "freq")
t <- 10
getStationaryLaw(dmm,pos=t)
##         a         c         g         t 
## 0.1903423 0.1122236 0.3365886 0.3608455
getStationaryLaw(dmm,all.pos=TRUE)
##                 a          c          g         t
## pos 1  0.06481662 0.02818511 0.40326808 0.5037302
## pos 2  0.07790480 0.03885048 0.39669639 0.4865483
## pos 3  0.09117643 0.04921663 0.38993838 0.4696686
## pos 4  0.10464358 0.05927103 0.38298537 0.4531000
## pos 5  0.11831915 0.06900023 0.37582801 0.4368526
## pos 6  0.13221693 0.07838983 0.36845611 0.4209371
## pos 7  0.14635168 0.08742431 0.36085867 0.4053653
## pos 8  0.16073924 0.09608699 0.35302375 0.3901500
## pos 9  0.17539667 0.10435990 0.34493841 0.3753050
## pos 10 0.19034229 0.11222359 0.33658858 0.3608455
## pos 11 0.20559591 0.11965708 0.32795900 0.3467880
## pos 12 0.22117889 0.12663761 0.31903307 0.3331504
## pos 13 0.23711438 0.13314051 0.30979273 0.3199524
## pos 14 0.25342749 0.13913895 0.30021829 0.3072153
## pos 15 0.27014550 0.14460373 0.29028827 0.2949625
## pos 16 0.28729811 0.14950300 0.27997918 0.2832197
## pos 17 0.30491773 0.15380194 0.26926532 0.2720150
## pos 18 0.32303979 0.15746244 0.25811850 0.2613793
## pos 19 0.34170313 0.16044268 0.24650775 0.2513464
## pos 20 0.36095038 0.16269666 0.23439898 0.2419540
## pos 21 0.38082851 0.16417367 0.22175459 0.2332432
## pos 22 0.40138934 0.16481771 0.20853300 0.2252600
## pos 23 0.42269019 0.16456673 0.19468814 0.2180549
## pos 24 0.44479470 0.16335182 0.18016881 0.2116847
## pos 25 0.46777368 0.16109626 0.16491796 0.2062121
## pos 26 0.49170614 0.15771431 0.14887187 0.2017077
## pos 27 0.51668056 0.15310994 0.13195912 0.1982504
## pos 28 0.54279637 0.14717520 0.11409940 0.1959290
## pos 29 0.57016562 0.13978827 0.09520211 0.1948440

Analysis of a model

Once a Markov drifting model has been estimated/constructed as described at the beginning of this section, the obtained model can be analyzed by means of several functions.

The computation of word probabilities according to an estimated/constructed DMM is carried out by means of the functions word_probability, word_probabilities and words_probabilities.

The function word_probability computes the probability of a word at a given position; it has the following arguments:

word: A word, i.e., a subsequence string of characters
pos: A position of the word along the sequence (numeric)
x: An object of class dmm
output_file: A file containing the probability
internal: FALSE (default) ; TRUE (for internal use of word applications)

It returns the numerical value of the probability.

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq")
word_probability("cgt",10,dmm,output_file="file.txt")
##        cgt 
## 0.01563115

The function word_probabilities computes the probabilities of a word at given positions. It has the following arguments:

word: A word, i.e., a subsequence string of characters
pos: Vector of integer positions of the word along the sequence; it is given by a start and end point
x: An object of class dmm
output_file: A file containing the probabilities
internal: FALSE (default) ; TRUE (for internal use of word applications)
plot: display a figure plot of word probabilities along the positions if TRUE

It returns a numerical vector of probabilities computed at the positions given in pos.

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq", fit.method="sum")
res <- word_probabilities("cgt", c(100, length(lambda)-3), dmm, output_file="file.txt", plot=TRUE)
head(res[[1]], n=10)
##    position probability
## 1       100  0.01562696
## 2       101  0.01562692
## 3       102  0.01562687
## 4       103  0.01562682
## 5       104  0.01562678
## 6       105  0.01562673
## 7       106  0.01562668
## 8       107  0.01562664
## 9       108  0.01562659
## 10      109  0.01562654
res[2]
## [[1]]

The function words_probabilities computes the probabilities of a word at given positions; it has the following arguments:

words: A vector of characters containing words
pos: Vector of integer positions of the word along the sequence; it is given by a start and end point
x: An object of class dmm
output_file: A file containing the matrix of probabilities
plot: display a figure plot of word probabilities along the positions if TRUE

It returns a data frame of probabilities computed for each element of words at the positions given in pos.

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq")
res <- words_probabilities(c("atcgattc", "taggct", "ggatcgg"), c(100, length(lambda)-8), dmm, output_file="file.txt", plot=TRUE)
head(res[[1]], n=10)
res[2]

The function lengthWord_probabilities computes the probabilities of occurrence of the observed word of given size in a sequence at several positions. This function has the following arguments:

n: Integer, the given length of the word
sequence: Vector of characters representing the sequence
pos: Vector of integer positions of the word along the sequence. It it is given by a start and end point
x: An object of class dmm
output_file A file containing the vector of probabilities
plot display several figure plots of probabilities of appearance of words along the positions if TRUE

It returns a data frame of probability by position

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq")
res <- lengthWord_probabilities(2, lambda, c(100, length(lambda)-2), dmm, output_file="file.txt", plot=TRUE)
res[2]
## [[1]]
## [[1]][[1]]

## 
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## 
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Simulation of drifting Markov models

The simulation of drifting Markov models is carried out by the function simulation that has the following arguments:

DRIMM: An object of class dmm
output_file: File containing the simulated sequence
model_size: Integer, the size of the model

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'), init.estim = "freq")
# simulate a sequence of length 20 000 from dmm
simulate(dmm, "file.txt", 20000)
## [1] "Write a simulated file from the model"
##     [1] "c" "a" "a" "c" "g" "c" "a" "a" "g" "a" "g" "g" "g" "t" "g" "t" "g" "a"
##    [19] "g" "g" "t" "g" "c" "a" "a" "c" "c" "a" "g" "g" "c" "t" "t" "g" "a" "c"
##    [37] "t" "t" "t" "g" "a" "c" "a" "c" "a" "t" "g" "t" "t" "g" "a" "c" "g" "g"
##    [55] "c" "t" "g" "c" "c" "t" "a" "c" "a" "a" "g" "c" "c" "t" "a" "a" "a" "t"
##    [73] "c" "g" "g" "g" "c" "a" "g" "g" "a" "g" "c" "g" "a" "c" "c" "g" "t" "a"
##    [91] "g" "t" "g" "t" "g" "t" "a" "c" "c" "g" "g" "c" "t" "c" "g" "c" "g" "c"
##   [109] "g" "g" "t" "c" "t" "g" "a" "a" "c" "t" "a" "g" "t" "t" "a" "a" "g" "a"
##   [127] "t" "c" "c" "g" "c" "g" "g" "t" "c" "t" "c" "c" "a" "c" "g" "g" "t" "t"
##   [145] "g" "c" "c" "c" "g" "g" "t" "c" "c" "a" "t" "g" "g" "g" "g" "a" "a" "a"
##   [163] "c" "g" "g" "g" "c" "c" "g" "g" "t" "t" "a" "c" "c" "g" "t" "a" "g" "g"
##   [181] "g" "g" "t" "g" "g" "c" "c" "c" "a" "g" "c" "t" "a" "t" "a" "g" "a" "t"
##   [199] "a" "g" "c" "c" "c" "a" "g" "c" "a" "c" "c" "a" "g" "c" "a" "g" "a" "c"
##   [217] "t" "g" "a" "g" "g" "c" "g" "c" "g" "a" "a" "a" "g" "t" "g" "a" "g" "c"
##   [235] "t" "g" "c" "g" "t" "c" "a" "c" "c" "a" "g" "g" "a" "g" "t" "g" "g" "a"
##   [253] "a" "a" "g" "g" "g" "t" "t" "t" "g" "t" "t" "t" "t" "g" "c" "g" "a" "t"
##   [271] "g" "g" "c" "t" "c" "c" "g" "t" "g" "a" "t" "g" "a" "a" "a" "g" "c" "t"
##   [289] "a" "c" "a" "g" "t" "a" "g" "g" "c" "g" "a" "t" "g" "t" "g" "t" "a" "t"
##   [307] "t" "g" "t" "t" "c" "a" "a" "t" "a" "t" "g" "a" "g" "g" "t" "g" "c" "a"
##   [325] "a" "a" "a" "g" "c" "a" "a" "c" "t" "c" "c" "c" "c" "a" "g" "g" "c" "g"
##   [343] "g" "g" "a" "a" "a" "a" "a" "c" "c" "a" "t" "t" "t" "a" "a" "t" "g" "a"
##   [361] "g" "a" "c" "c" "g" "a" "c" "c" "c" "c" "c" "g" "g" "g" "c" "c" "g" "c"
##   [379] "g" "g" "c" "g" "a" "a" "g" "g" "a" "a" "c" "c" "a" "t" "t" "c" "g" "g"
##   [397] "a" "a" "a" "g" "t" "c" "a" "g" "g" "a" "c" "t" "a" "c" "a" "t" "g" "t"
##   [415] "c" "a" "g" "c" "g" "t" "a" "t" "a" "c" "t" "a" "t" "a" "t" "c" "g" "c"
##   [433] "g" "g" "g" "g" "t" "t" "c" "t" "t" "g" "c" "t" "t" "a" "t" "c" "a" "c"
##   [451] "t" "a" "g" "g" "g" "c" "c" "a" "a" "t" "a" "a" "a" "g" "g" "t" "c" "c"
##   [469] "g" "g" "c" "c" "c" "t" "g" "c" "a" "g" "g" "a" "g" "c" "g" "t" "g" "t"
##   [487] "c" "c" "g" "c" "c" "t" "g" "c" "c" "g" "a" "g" "g" "c" "g" "g" "g" "a"
##   [505] "g" "a" "t" "g" "g" "c" "a" "g" "t" "g" "a" "a" "g" "g" "a" "a" "c" "g"
##   [523] "c" "c" "c" "c" "c" "a" "a" "c" "g" "g" "c" "g" "a" "g" "g" "a" "t" "c"
##   [541] "c" "g" "c" "g" "g" "c" "c" "g" "a" "c" "c" "t" "t" "t" "g" "g" "a" "c"
##   [559] "c" "c" "g" "a" "g" "g" "t" "g" "a" "c" "a" "g" "a" "a" "a" "g" "g" "a"
##   [577] "c" "g" "g" "c" "c" "t" "g" "t" "g" "g" "c" "c" "g" "a" "a" "g" "t" "a"
##   [595] "a" "a" "g" "a" "t" "g" "g" "c" "g" "c" "g" "t" "c" "a" "g" "g" "g" "a"
##   [613] "g" "g" "a" "c" "t" "c" "g" "g" "g" "c" "a" "t" "a" "a" "g" "a" "g" "g"
##   [631] "t" "g" "g" "a" "a" "g" "g" "g" "a" "t" "t" "c" "g" "c" "t" "g" "a" "c"
##   [649] "t" "g" "g" "t" "g" "t" "c" "c" "a" "a" "g" "t" "g" "a" "t" "g" "a" "g"
##   [667] "g" "c" "t" "t" "g" "a" "c" "c" "t" "g" "c" "c" "g" "t" "g" "a" "t" "g"
##   [685] "a" "a" "c" "t" "g" "a" "g" "c" "c" "a" "c" "a" "a" "g" "t" "t" "g" "c"
##   [703] "g" "g" "t" "t" "g" "t" "g" "c" "t" "g" "c" "a" "g" "a" "g" "a" "g" "a"
##   [721] "t" "a" "c" "a" "a" "g" "g" "g" "c" "c" "g" "c" "g" "g" "g" "t" "a" "g"
##   [739] "g" "g" "t" "g" "c" "a" "g" "g" "a" "c" "c" "g" "t" "a" "t" "t" "t" "t"
##   [757] "c" "g" "c" "c" "a" "a" "a" "t" "a" "t" "t" "a" "c" "g" "c" "a" "g" "g"
##   [775] "g" "g" "t" "g" "g" "g" "g" "c" "c" "t" "t" "g" "c" "g" "a" "g" "g" "g"
##   [793] "t" "g" "g" "g" "g" "c" "c" "a" "g" "c" "c" "a" "t" "g" "a" "t" "g" "t"
##   [811] "a" "a" "g" "a" "c" "g" "g" "c" "a" "t" "a" "g" "c" "t" "c" "g" "c" "t"
##   [829] "a" "c" "a" "a" "c" "g" "c" "c" "a" "g" "c" "g" "c" "t" "g" "c" "g" "c"
##   [847] "a" "g" "c" "g" "a" "g" "t" "g" "a" "t" "c" "t" "a" "a" "g" "g" "t" "a"
##   [865] "c" "a" "g" "a" "g" "g" "g" "a" "t" "g" "a" "g" "t" "g" "a" "t" "a" "t"
##   [883] "g" "c" "a" "c" "g" "c" "t" "a" "a" "a" "g" "c" "g" "a" "a" "t" "a" "c"
##   [901] "t" "a" "g" "c" "a" "g" "a" "a" "c" "c" "g" "c" "c" "c" "g" "c" "a" "g"
##   [919] "g" "g" "a" "a" "t" "a" "c" "c" "c" "a" "a" "g" "c" "g" "c" "t" "a" "t"
##   [937] "g" "c" "a" "g" "t" "a" "g" "t" "g" "g" "c" "g" "a" "a" "c" "g" "g" "g"
##   [955] "c" "t" "c" "a" "g" "t" "c" "g" "c" "c" "g" "a" "a" "g" "g" "c" "g" "a"
##   [973] "g" "g" "g" "t" "t" "t" "c" "g" "a" "g" "g" "c" "a" "a" "a" "a" "c" "t"
##   [991] "g" "t" "t" "a" "t" "g" "c" "a" "c" "a" "g" "t" "g" "c" "g" "c" "a" "a"
##  [1009] "g" "c" "a" "c" "c" "a" "c" "g" "g" "g" "t" "t" "c" "t" "g" "t" "t" "a"
##  [1027] "a" "g" "g" "c" "c" "g" "g" "t" "c" "g" "t" "t" "c" "a" "g" "t" "g" "g"
##  [1045] "g" "c" "c" "g" "a" "c" "g" "t" "t" "g" "t" "t" "t" "c" "c" "c" "c" "g"
##  [1063] "g" "g" "c" "t" "g" "c" "g" "a" "g" "c" "c" "c" "g" "t" "c" "c" "g" "t"
##  [1081] "c" "g" "g" "g" "a" "c" "g" "a" "a" "c" "a" "g" "g" "g" "t" "g" "a" "c"
##  [1099] "g" "g" "a" "t" "g" "a" "g" "t" "c" "a" "a" "g" "g" "t" "g" "g" "a" "g"
##  [1117] "c" "a" "c" "a" "c" "c" "g" "t" "g" "g" "t" "g" "t" "t" "g" "t" "c" "a"
##  [1135] "c" "a" "t" "g" "g" "g" "c" "g" "c" "g" "g" "a" "g" "t" "c" "t" "t" "t"
##  [1153] "c" "a" "g" "a" "t" "c" "a" "a" "t" "c" "c" "a" "g" "c" "g" "g" "c" "t"
##  [1171] "a" "g" "c" "c" "c" "a" "a" "g" "c" "a" "a" "a" "g" "g" "a" "t" "g" "a"
##  [1189] "g" "c" "g" "c" "a" "g" "g" "g" "c" "g" "t" "g" "c" "c" "g" "g" "t" "t"
##  [1207] "c" "t" "c" "g" "g" "t" "c" "g" "c" "c" "g" "c" "g" "t" "t" "a" "a" "g"
##  [1225] "c" "g" "a" "g" "a" "a" "a" "c" "t" "g" "a" "g" "g" "a" "g" "c" "a" "a"
##  [1243] "t" "g" "a" "a" "a" "a" "t" "g" "c" "g" "c" "a" "a" "a" "a" "g" "g" "a"
##  [1261] "c" "g" "a" "a" "g" "a" "g" "c" "g" "a" "c" "c" "g" "a" "g" "g" "g" "c"
##  [1279] "c" "t" "c" "g" "g" "g" "g" "a" "g" "a" "g" "t" "a" "g" "c" "g" "c" "t"
##  [1297] "t" "c" "c" "g" "c" "t" "a" "a" "a" "a" "c" "g" "g" "c" "t" "t" "g" "g"
##  [1315] "g" "t" "a" "a" "a" "a" "a" "c" "g" "a" "g" "c" "t" "g" "g" "a" "g" "t"
##  [1333] "g" "c" "c" "t" "a" "c" "t" "a" "a" "c" "t" "t" "c" "g" "c" "c" "g" "c"
##  [1351] "g" "t" "c" "c" "a" "a" "g" "g" "g" "a" "t" "g" "c" "a" "c" "t" "c" "t"
##  [1369] "c" "c" "a" "g" "a" "c" "g" "g" "g" "t" "c" "a" "c" "c" "c" "g" "c" "a"
##  [1387] "c" "g" "t" "g" "t" "c" "a" "g" "g" "c" "t" "a" "g" "c" "g" "c" "g" "a"
##  [1405] "t" "a" "c" "a" "g" "c" "g" "g" "a" "c" "g" "c" "c" "g" "t" "g" "t" "a"
##  [1423] "a" "g" "g" "a" "c" "a" "t" "a" "c" "a" "a" "t" "a" "c" "a" "a" "c" "g"
##  [1441] "c" "g" "c" "g" "t" "c" "c" "g" "g" "g" "a" "c" "a" "g" "c" "a" "a" "t"
##  [1459] "c" "c" "g" "c" "t" "g" "g" "g" "g" "t" "g" "t" "c" "g" "g" "g" "c" "a"
##  [1477] "t" "a" "c" "g" "g" "a" "a" "g" "t" "c" "a" "c" "c" "a" "t" "a" "g" "c"
##  [1495] "a" "g" "g" "g" "t" "c" "t" "c" "g" "g" "g" "c" "a" "t" "a" "c" "t" "g"
##  [1513] "a" "c" "a" "g" "a" "g" "t" "g" "g" "c" "a" "c" "t" "g" "t" "t" "a" "t"
##  [1531] "a" "t" "g" "a" "g" "c" "a" "a" "c" "g" "g" "g" "t" "c" "g" "a" "a" "c"
##  [1549] "g" "c" "t" "g" "a" "g" "t" "t" "g" "g" "g" "g" "c" "t" "c" "a" "c" "t"
##  [1567] "g" "g" "c" "g" "a" "a" "g" "t" "a" "g" "c" "g" "t" "g" "t" "g" "t" "a"
##  [1585] "t" "c" "c" "a" "t" "g" "a" "t" "a" "g" "g" "t" "t" "g" "t" "c" "g" "g"
##  [1603] "t" "a" "c" "g" "c" "c" "c" "t" "a" "a" "c" "g" "c" "g" "a" "t" "g" "t"
##  [1621] "g" "g" "g" "c" "g" "c" "t" "a" "g" "g" "g" "a" "c" "a" "a" "g" "a" "g"
##  [1639] "g" "c" "g" "g" "c" "a" "a" "c" "t" "c" "a" "c" "t" "c" "a" "a" "c" "t"
##  [1657] "g" "c" "t" "g" "g" "g" "g" "t" "g" "c" "a" "g" "a" "c" "a" "c" "t" "c"
##  [1675] "g" "g" "a" "a" "c" "c" "c" "c" "a" "g" "t" "t" "c" "a" "c" "a" "g" "a"
##  [1693] "c" "t" "t" "c" "g" "g" "a" "t" "a" "g" "a" "c" "g" "c" "g" "g" "g" "g"
##  [1711] "t" "g" "g" "t" "c" "c" "a" "t" "c" "g" "g" "a" "t" "t" "a" "g" "a" "g"
##  [1729] "g" "t" "c" "g" "a" "t" "g" "a" "g" "t" "t" "a" "c" "a" "c" "t" "a" "g"
##  [1747] "c" "g" "t" "g" "c" "c" "g" "a" "c" "c" "g" "c" "c" "g" "a" "t" "c" "c"
##  [1765] "g" "t" "t" "t" "c" "t" "g" "c" "c" "t" "c" "g" "g" "a" "t" "g" "c" "g"
##  [1783] "g" "c" "t" "t" "c" "a" "t" "c" "a" "c" "c" "g" "g" "g" "a" "a" "g" "a"
##  [1801] "g" "g" "g" "t" "a" "t" "t" "t" "t" "g" "c" "g" "a" "t" "g" "a" "g" "g"
##  [1819] "c" "c" "g" "g" "c" "g" "g" "g" "c" "g" "a" "a" "c" "g" "g" "g" "t" "a"
##  [1837] "c" "g" "a" "g" "a" "t" "c" "g" "t" "g" "g" "a" "c" "a" "a" "t" "c" "g"
##  [1855] "c" "g" "c" "t" "c" "g" "g" "t" "c" "g" "t" "a" "g" "a" "t" "g" "c" "c"
##  [1873] "a" "a" "c" "c" "c" "c" "t" "g" "g" "c" "a" "g" "c" "t" "g" "g" "g" "g"
##  [1891] "a" "g" "a" "c" "c" "g" "a" "a" "t" "g" "c" "a" "g" "t" "c" "c" "a" "c"
##  [1909] "a" "g" "g" "a" "t" "a" "g" "g" "c" "g" "a" "g" "t" "t" "a" "g" "c" "g"
##  [1927] "a" "c" "g" "t" "c" "g" "c" "g" "a" "c" "g" "g" "t" "g" "a" "g" "t" "g"
##  [1945] "t" "c" "t" "g" "g" "a" "c" "t" "g" "c" "g" "g" "a" "c" "g" "t" "c" "t"
##  [1963] "g" "a" "a" "a" "a" "a" "t" "g" "t" "g" "a" "c" "g" "t" "t" "c" "a" "a"
##  [1981] "a" "a" "c" "g" "t" "c" "t" "g" "g" "a" "a" "t" "g" "c" "a" "c" "g" "t"
##  [1999] "a" "a" "g" "a" "g" "g" "g" "t" "t" "a" "t" "c" "c" "g" "c" "a" "c" "g"
##  [2017] "t" "a" "g" "g" "a" "c" "c" "g" "t" "t" "c" "t" "c" "c" "t" "c" "c" "g"
##  [2035] "g" "g" "t" "g" "t" "g" "c" "c" "t" "a" "g" "t" "c" "t" "g" "t" "g" "c"
##  [2053] "g" "g" "g" "g" "t" "c" "a" "a" "t" "a" "a" "g" "t" "g" "a" "t" "g" "t"
##  [2071] "c" "a" "a" "c" "c" "t" "c" "g" "a" "t" "t" "t" "t" "c" "g" "c" "g" "c"
##  [2089] "a" "g" "g" "g" "g" "g" "g" "a" "c" "a" "a" "c" "a" "g" "a" "c" "a" "c"
##  [2107] "g" "c" "g" "c" "t" "g" "a" "t" "a" "a" "a" "t" "g" "c" "t" "a" "g" "c"
##  [2125] "a" "a" "t" "g" "a" "g" "a" "g" "t" "c" "t" "a" "g" "g" "a" "t" "a" "a"
##  [2143] "g" "a" "a" "c" "c" "c" "c" "c" "a" "a" "g" "g" "g" "g" "a" "a" "t" "g"
##  [2161] "g" "g" "t" "g" "c" "g" "c" "g" "t" "a" "c" "t" "g" "g" "a" "g" "a" "c"
##  [2179] "g" "a" "a" "a" "t" "g" "c" "g" "g" "t" "c" "g" "c" "g" "c" "t" "a" "t"
##  [2197] "g" "t" "t" "g" "a" "c" "c" "t" "c" "a" "c" "t" "a" "a" "a" "c" "c" "a"
##  [2215] "c" "g" "a" "c" "t" "a" "t" "g" "t" "t" "c" "t" "t" "a" "g" "g" "a" "t"
##  [2233] "g" "a" "c" "g" "c" "t" "g" "g" "c" "a" "g" "a" "g" "t" "g" "g" "a" "a"
##  [2251] "a" "c" "t" "t" "g" "a" "a" "c" "c" "a" "g" "c" "a" "g" "t" "g" "g" "g"
##  [2269] "c" "a" "a" "c" "c" "g" "a" "t" "g" "a" "g" "g" "g" "a" "a" "a" "a" "g"
##  [2287] "c" "c" "t" "c" "g" "a" "c" "c" "a" "a" "g" "c" "c" "t" "a" "g" "t" "a"
##  [2305] "g" "c" "a" "a" "g" "g" "a" "g" "t" "c" "t" "c" "a" "t" "g" "g" "c" "a"
##  [2323] "a" "g" "t" "g" "c" "c" "g" "g" "g" "g" "g" "a" "a" "a" "a" "g" "t" "g"
##  [2341] "g" "g" "a" "c" "a" "g" "g" "c" "c" "a" "g" "c" "a" "c" "c" "c" "c" "c"
##  [2359] "c" "g" "c" "c" "c" "g" "a" "t" "c" "c" "a" "c" "a" "a" "t" "g" "t" "g"
##  [2377] "a" "a" "g" "a" "t" "g" "t" "a" "g" "t" "t" "a" "a" "t" "t" "t" "a" "g"
##  [2395] "a" "t" "g" "c" "a" "c" "a" "c" "t" "g" "c" "c" "a" "g" "c" "g" "g" "t"
##  [2413] "t" "c" "a" "c" "g" "g" "t" "g" "t" "c" "a" "c" "c" "c" "a" "c" "a" "c"
##  [2431] "a" "c" "c" "g" "g" "g" "g" "a" "a" "t" "t" "t" "a" "g" "c" "a" "a" "c"
##  [2449] "t" "c" "a" "c" "g" "c" "a" "g" "g" "t" "g" "g" "g" "g" "a" "g" "t" "g"
##  [2467] "t" "g" "a" "a" "t" "t" "c" "g" "c" "t" "a" "a" "c" "t" "g" "g" "g" "c"
##  [2485] "g" "g" "t" "g" "c" "g" "c" "g" "a" "g" "a" "c" "t" "g" "g" "c" "c" "t"
##  [2503] "c" "a" "g" "c" "t" "t" "t" "g" "a" "g" "t" "g" "g" "g" "a" "t" "g" "c"
##  [2521] "g" "t" "t" "a" "a" "t" "g" "g" "a" "t" "a" "g" "a" "g" "c" "t" "t" "c"
##  [2539] "g" "g" "t" "g" "a" "a" "c" "c" "a" "a" "g" "c" "g" "g" "c" "a" "c" "g"
##  [2557] "c" "a" "a" "c" "c" "g" "g" "g" "t" "c" "t" "g" "c" "g" "t" "g" "c" "t"
##  [2575] "t" "g" "a" "c" "g" "c" "a" "g" "a" "a" "g" "a" "a" "t" "c" "g" "g" "t"
##  [2593] "g" "c" "t" "g" "c" "c" "a" "c" "g" "g" "g" "a" "g" "a" "c" "t" "g" "c"
##  [2611] "a" "c" "g" "t" "a" "c" "t" "g" "c" "a" "t" "a" "g" "g" "t" "t" "a" "g"
##  [2629] "a" "a" "g" "a" "a" "t" "t" "c" "g" "c" "c" "t" "a" "a" "c" "c" "g" "t"
##  [2647] "a" "g" "t" "g" "c" "g" "t" "t" "c" "a" "t" "c" "a" "a" "a" "c" "c" "g"
##  [2665] "g" "c" "g" "t" "c" "t" "a" "t" "a" "g" "t" "a" "c" "t" "g" "g" "g" "c"
##  [2683] "c" "g" "g" "g" "c" "g" "c" "a" "t" "t" "a" "a" "c" "t" "g" "a" "g" "g"
##  [2701] "g" "g" "g" "c" "g" "g" "t" "c" "a" "c" "g" "a" "t" "c" "c" "c" "c" "t"
##  [2719] "c" "g" "a" "g" "t" "g" "c" "a" "t" "a" "t" "t" "c" "a" "g" "a" "g" "c"
##  [2737] "a" "g" "g" "c" "g" "c" "c" "a" "a" "c" "g" "a" "t" "t" "a" "g" "a" "a"
##  [2755] "t" "c" "t" "c" "g" "g" "g" "g" "g" "g" "t" "c" "a" "a" "c" "t" "g" "t"
##  [2773] "g" "g" "g" "c" "c" "g" "g" "t" "t" "g" "t" "a" "a" "t" "g" "t" "c" "c"
##  [2791] "a" "t" "g" "t" "g" "g" "g" "t" "g" "t" "c" "a" "g" "a" "a" "c" "t" "g"
##  [2809] "a" "g" "t" "t" "c" "t" "t" "t" "a" "a" "a" "c" "g" "g" "c" "c" "g" "c"
##  [2827] "g" "a" "a" "a" "c" "a" "a" "g" "a" "g" "a" "c" "g" "g" "t" "g" "c" "c"
##  [2845] "g" "g" "a" "a" "g" "a" "c" "g" "a" "t" "g" "g" "c" "g" "a" "c" "a" "c"
##  [2863] "c" "a" "c" "g" "c" "g" "t" "c" "a" "c" "g" "t" "c" "g" "a" "t" "t" "g"
##  [2881] "a" "t" "c" "c" "t" "c" "t" "g" "g" "a" "g" "t" "g" "c" "a" "c" "a" "a"
##  [2899] "c" "t" "g" "g" "t" "g" "c" "g" "g" "t" "g" "c" "c" "c" "g" "a" "c" "g"
##  [2917] "t" "g" "t" "c" "t" "c" "t" "g" "a" "c" "g" "c" "c" "a" "c" "t" "t" "t"
##  [2935] "a" "g" "t" "a" "a" "t" "a" "t" "c" "g" "g" "t" "a" "a" "a" "a" "a" "g"
##  [2953] "c" "t" "a" "g" "g" "g" "t" "t" "c" "g" "a" "g" "t" "g" "g" "g" "c" "c"
##  [2971] "t" "t" "c" "c" "a" "a" "g" "c" "c" "g" "g" "t" "t" "t" "g" "g" "a" "g"
##  [2989] "a" "g" "a" "c" "g" "g" "t" "g" "a" "a" "c" "t" "c" "t" "g" "c" "c" "c"
##  [3007] "a" "g" "c" "c" "g" "c" "a" "c" "g" "g" "g" "g" "c" "a" "c" "c" "c" "t"
##  [3025] "t" "a" "c" "g" "c" "c" "a" "g" "a" "g" "g" "t" "g" "a" "c" "t" "c" "g"
##  [3043] "g" "g" "t" "c" "c" "t" "t" "g" "g" "a" "a" "g" "t" "t" "g" "c" "t" "g"
##  [3061] "g" "a" "g" "t" "a" "c" "t" "a" "c" "a" "c" "g" "c" "g" "c" "g" "c" "t"
##  [3079] "c" "a" "c" "a" "a" "g" "c" "g" "g" "a" "c" "t" "g" "a" "g" "c" "c" "c"
##  [3097] "c" "t" "a" "a" "g" "t" "t" "g" "t" "g" "c" "c" "t" "t" "a" "g" "g" "t"
##  [3115] "c" "g" "c" "g" "a" "t" "g" "a" "t" "g" "a" "g" "a" "g" "a" "g" "t" "g"
##  [3133] "t" "a" "a" "a" "a" "a" "g" "a" "c" "c" "t" "c" "a" "g" "a" "a" "g" "a"
##  [3151] "c" "g" "g" "a" "t" "a" "a" "c" "a" "g" "c" "c" "c" "a" "t" "a" "t" "t"
##  [3169] "c" "a" "c" "a" "g" "c" "g" "g" "g" "g" "c" "c" "g" "c" "c" "g" "t" "a"
##  [3187] "c" "a" "g" "a" "t" "g" "t" "t" "t" "c" "c" "c" "g" "g" "a" "a" "a" "c"
##  [3205] "g" "a" "a" "a" "g" "a" "g" "t" "g" "t" "g" "t" "t" "c" "a" "g" "c" "a"
##  [3223] "a" "c" "g" "g" "a" "g" "g" "t" "g" "a" "g" "g" "c" "c" "g" "g" "g" "g"
##  [3241] "a" "g" "g" "c" "t" "g" "a" "c" "g" "c" "t" "c" "a" "a" "a" "t" "g" "a"
##  [3259] "a" "g" "t" "c" "a" "g" "c" "g" "a" "t" "c" "c" "c" "a" "g" "a" "t" "t"
##  [3277] "t" "g" "g" "t" "g" "a" "g" "a" "g" "c" "t" "a" "c" "c" "t" "g" "c" "g"
##  [3295] "t" "c" "c" "g" "c" "g" "g" "g" "g" "g" "a" "g" "a" "c" "g" "c" "t" "g"
##  [3313] "g" "t" "c" "t" "c" "t" "t" "c" "c" "a" "g" "a" "a" "a" "a" "g" "c" "a"
##  [3331] "g" "g" "c" "a" "a" "g" "a" "g" "a" "t" "a" "c" "g" "a" "g" "c" "g" "t"
##  [3349] "c" "c" "g" "g" "g" "g" "c" "g" "a" "t" "c" "g" "g" "a" "t" "a" "t" "a"
##  [3367] "a" "g" "g" "g" "g" "c" "t" "t" "g" "c" "g" "a" "a" "g" "a" "t" "t" "c"
##  [3385] "c" "a" "a" "t" "t" "a" "g" "g" "t" "g" "g" "a" "t" "c" "g" "t" "t" "g"
##  [3403] "a" "c" "t" "c" "t" "g" "g" "t" "t" "a" "t" "a" "c" "a" "t" "g" "c" "c"
##  [3421] "t" "c" "c" "g" "g" "g" "g" "t" "t" "t" "c" "g" "a" "g" "g" "a" "c" "g"
##  [3439] "t" "a" "g" "g" "t" "t" "g" "g" "g" "g" "t" "g" "c" "g" "g" "t" "t" "a"
##  [3457] "a" "c" "g" "a" "a" "c" "g" "g" "g" "g" "g" "g" "t" "t" "c" "g" "t" "c"
##  [3475] "a" "a" "g" "a" "g" "a" "c" "t" "g" "c" "g" "g" "a" "g" "t" "a" "a" "a"
##  [3493] "a" "a" "a" "t" "c" "a" "g" "g" "a" "c" "g" "t" "g" "g" "t" "t" "a" "t"
##  [3511] "g" "t" "g" "g" "c" "a" "t" "g" "c" "g" "g" "a" "g" "a" "c" "c" "g" "a"
##  [3529] "c" "c" "c" "a" "a" "a" "a" "g" "g" "a" "a" "c" "a" "t" "g" "a" "t" "t"
##  [3547] "a" "t" "a" "c" "a" "t" "c" "a" "g" "g" "c" "c" "g" "t" "c" "c" "a" "g"
##  [3565] "a" "g" "g" "a" "c" "c" "a" "t" "t" "g" "c" "g" "a" "g" "t" "g" "g" "g"
##  [3583] "a" "a" "t" "a" "g" "g" "c" "c" "g" "g" "t" "c" "c" "g" "c" "a" "a" "g"
##  [3601] "c" "c" "c" "g" "c" "g" "c" "c" "c" "c" "a" "a" "g" "t" "g" "c" "a" "c"
##  [3619] "a" "c" "g" "g" "t" "c" "c" "g" "t" "a" "g" "t" "g" "t" "g" "c" "c" "a"
##  [3637] "a" "g" "a" "g" "g" "g" "a" "t" "a" "g" "g" "g" "a" "a" "t" "g" "g" "a"
##  [3655] "c" "c" "g" "t" "g" "g" "t" "g" "a" "c" "a" "g" "a" "a" "c" "c" "a" "t"
##  [3673] "c" "c" "g" "a" "a" "g" "g" "a" "t" "a" "g" "a" "c" "a" "a" "g" "c" "g"
##  [3691] "t" "g" "a" "c" "t" "t" "c" "g" "a" "g" "t" "c" "t" "g" "c" "a" "g" "t"
##  [3709] "t" "a" "t" "c" "g" "a" "t" "g" "c" "a" "a" "t" "a" "c" "t" "g" "c" "t"
##  [3727] "a" "t" "t" "a" "a" "t" "g" "c" "g" "a" "a" "a" "c" "a" "g" "a" "a" "t"
##  [3745] "c" "a" "g" "a" "g" "g" "c" "c" "c" "a" "c" "a" "t" "c" "a" "c" "c" "c"
##  [3763] "c" "c" "c" "c" "g" "g" "g" "c" "g" "c" "g" "a" "c" "g" "c" "g" "t" "a"
##  [3781] "t" "t" "a" "g" "g" "t" "a" "c" "a" "g" "t" "g" "g" "a" "a" "a" "a" "a"
##  [3799] "t" "g" "t" "g" "t" "g" "t" "a" "c" "g" "a" "t" "c" "t" "c" "g" "g" "g"
##  [3817] "g" "a" "g" "t" "t" "g" "g" "a" "t" "c" "a" "g" "g" "t" "a" "c" "c" "g"
##  [3835] "a" "g" "c" "a" "t" "c" "a" "c" "g" "c" "c" "c" "c" "t" "c" "g" "c" "t"
##  [3853] "t" "c" "a" "c" "g" "a" "c" "a" "a" "a" "g" "a" "c" "c" "t" "c" "g" "a"
##  [3871] "a" "g" "c" "c" "t" "g" "t" "g" "t" "g" "c" "c" "g" "a" "g" "a" "g" "a"
##  [3889] "c" "a" "c" "g" "t" "a" "g" "g" "c" "a" "t" "t" "c" "t" "g" "a" "t" "g"
##  [3907] "g" "c" "a" "c" "c" "g" "a" "g" "c" "a" "g" "a" "t" "t" "g" "c" "c" "a"
##  [3925] "a" "c" "c" "c" "c" "t" "c" "c" "c" "c" "g" "g" "c" "g" "t" "g" "g" "g"
##  [3943] "t" "g" "t" "t" "c" "a" "a" "c" "c" "g" "c" "c" "a" "t" "a" "g" "g" "t"
##  [3961] "c" "g" "a" "c" "g" "g" "t" "g" "g" "g" "c" "g" "c" "t" "g" "t" "a" "c"
##  [3979] "a" "t" "a" "c" "g" "a" "c" "a" "c" "a" "a" "t" "t" "c" "c" "a" "g" "g"
##  [3997] "g" "g" "a" "t" "t" "c" "g" "c" "t" "c" "g" "t" "t" "g" "c" "c" "g" "t"
##  [4015] "a" "c" "g" "a" "c" "c" "a" "a" "t" "a" "g" "a" "a" "c" "g" "c" "g" "c"
##  [4033] "c" "t" "g" "a" "g" "g" "g" "a" "g" "t" "c" "g" "a" "c" "t" "g" "g" "g"
##  [4051] "t" "a" "g" "t" "g" "g" "t" "g" "c" "g" "t" "a" "t" "a" "c" "g" "g" "a"
##  [4069] "a" "g" "t" "t" "t" "c" "c" "a" "g" "a" "c" "c" "c" "a" "t" "g" "t" "a"
##  [4087] "t" "t" "a" "g" "g" "g" "t" "t" "g" "t" "t" "c" "t" "c" "g" "g" "c" "a"
##  [4105] "g" "c" "c" "g" "g" "a" "a" "t" "c" "t" "t" "g" "t" "a" "a" "g" "g" "t"
##  [4123] "a" "a" "g" "c" "a" "t" "c" "a" "g" "c" "g" "a" "t" "g" "t" "c" "a" "g"
##  [4141] "a" "a" "a" "a" "g" "t" "c" "a" "g" "g" "t" "g" "t" "a" "a" "g" "t" "a"
##  [4159] "t" "t" "g" "t" "a" "t" "c" "t" "c" "a" "t" "t" "t" "a" "g" "g" "a" "c"
##  [4177] "a" "a" "t" "a" "a" "a" "g" "c" "a" "g" "g" "a" "c" "a" "t" "t" "c" "t"
##  [4195] "a" "c" "g" "t" "g" "c" "c" "a" "t" "a" "g" "c" "g" "g" "c" "c" "a" "t"
##  [4213] "c" "c" "g" "g" "g" "g" "g" "t" "g" "t" "g" "g" "a" "g" "c" "a" "a" "g"
##  [4231] "g" "a" "g" "c" "g" "g" "c" "a" "c" "a" "t" "t" "g" "a" "a" "g" "a" "g"
##  [4249] "t" "g" "g" "g" "c" "a" "g" "g" "c" "a" "c" "c" "a" "c" "a" "g" "t" "g"
##  [4267] "g" "g" "a" "a" "a" "g" "t" "g" "g" "a" "g" "t" "t" "g" "a" "c" "c" "a"
##  [4285] "c" "g" "g" "g" "a" "g" "g" "g" "t" "a" "t" "g" "c" "c" "c" "g" "a" "c"
##  [4303] "c" "g" "c" "t" "c" "c" "c" "g" "g" "g" "g" "a" "t" "a" "t" "c" "c" "t"
##  [4321] "g" "g" "a" "g" "a" "g" "g" "c" "a" "a" "g" "a" "a" "t" "a" "g" "t" "t"
##  [4339] "c" "a" "g" "c" "a" "a" "g" "g" "t" "t" "g" "a" "c" "g" "c" "a" "t" "g"
##  [4357] "g" "g" "g" "g" "g" "t" "a" "g" "g" "c" "a" "a" "t" "a" "g" "g" "a" "g"
##  [4375] "a" "t" "t" "g" "g" "g" "g" "t" "t" "c" "g" "a" "a" "t" "a" "g" "g" "c"
##  [4393] "c" "g" "a" "g" "c" "c" "g" "c" "t" "c" "g" "g" "t" "c" "t" "g" "a" "c"
##  [4411] "t" "g" "a" "t" "t" "g" "g" "a" "c" "c" "a" "g" "a" "a" "a" "t" "c" "t"
##  [4429] "a" "a" "c" "c" "t" "g" "c" "c" "c" "a" "c" "g" "c" "a" "a" "a" "g" "c"
##  [4447] "g" "g" "g" "c" "g" "c" "g" "a" "c" "g" "g" "a" "g" "a" "g" "a" "c" "c"
##  [4465] "a" "a" "t" "a" "g" "t" "a" "t" "a" "g" "g" "a" "g" "c" "g" "g" "a" "g"
##  [4483] "a" "c" "g" "g" "c" "t" "g" "g" "g" "t" "c" "g" "a" "c" "g" "g" "t" "c"
##  [4501] "t" "a" "a" "c" "g" "a" "g" "a" "g" "c" "a" "g" "t" "t" "c" "a" "a" "c"
##  [4519] "a" "g" "c" "t" "t" "g" "g" "a" "t" "t" "a" "c" "c" "c" "a" "t" "c" "t"
##  [4537] "c" "g" "g" "g" "g" "c" "g" "a" "c" "a" "a" "c" "g" "g" "a" "g" "c" "g"
##  [4555] "a" "t" "a" "g" "g" "g" "a" "a" "g" "g" "t" "c" "a" "g" "c" "t" "c" "t"
##  [4573] "a" "g" "c" "g" "a" "a" "g" "c" "g" "c" "t" "a" "g" "c" "g" "a" "c" "c"
##  [4591] "g" "g" "a" "g" "c" "c" "c" "c" "g" "c" "t" "a" "g" "g" "g" "a" "c" "a"
##  [4609] "c" "g" "t" "a" "c" "t" "g" "a" "g" "c" "a" "c" "t" "g" "g" "t" "a" "g"
##  [4627] "a" "c" "t" "g" "a" "g" "a" "g" "t" "a" "g" "a" "a" "g" "g" "g" "g" "g"
##  [4645] "t" "g" "t" "a" "c" "a" "t" "a" "g" "a" "c" "t" "a" "a" "a" "a" "a" "t"
##  [4663] "g" "c" "t" "c" "c" "c" "t" "g" "g" "a" "c" "a" "t" "c" "g" "a" "g" "c"
##  [4681] "g" "a" "g" "a" "t" "a" "g" "c" "g" "c" "t" "c" "g" "t" "c" "g" "g" "c"
##  [4699] "a" "a" "g" "g" "t" "t" "g" "t" "c" "c" "g" "g" "g" "c" "c" "a" "g" "c"
##  [4717] "a" "a" "g" "t" "g" "c" "g" "g" "a" "a" "t" "a" "c" "c" "g" "a" "c" "g"
##  [4735] "c" "g" "t" "g" "a" "t" "c" "c" "c" "a" "a" "g" "t" "c" "c" "g" "a" "g"
##  [4753] "c" "c" "g" "c" "g" "a" "a" "g" "a" "g" "a" "g" "g" "a" "g" "a" "g" "g"
##  [4771] "a" "t" "t" "c" "c" "c" "c" "g" "g" "g" "g" "t" "t" "a" "g" "g" "t" "g"
##  [4789] "a" "c" "t" "t" "g" "t" "g" "a" "t" "t" "g" "g" "c" "g" "g" "a" "t" "c"
##  [4807] "c" "a" "c" "g" "c" "a" "t" "t" "t" "t" "a" "g" "t" "a" "t" "a" "t" "c"
##  [4825] "g" "a" "g" "a" "a" "a" "c" "c" "g" "a" "t" "g" "g" "t" "a" "c" "g" "g"
##  [4843] "c" "a" "g" "g" "g" "a" "g" "g" "a" "g" "c" "g" "c" "g" "t" "c" "a" "g"
##  [4861] "g" "c" "t" "g" "t" "a" "g" "c" "g" "g" "c" "a" "t" "a" "g" "t" "g" "g"
##  [4879] "t" "t" "g" "c" "a" "t" "c" "a" "a" "a" "g" "t" "c" "a" "t" "g" "t" "g"
##  [4897] "c" "a" "g" "g" "g" "a" "t" "a" "g" "a" "g" "a" "c" "a" "g" "g" "c" "a"
##  [4915] "a" "a" "a" "c" "g" "g" "t" "c" "a" "g" "c" "a" "a" "t" "t" "a" "g" "c"
##  [4933] "c" "g" "a" "t" "a" "a" "t" "g" "g" "c" "c" "g" "a" "c" "c" "t" "g" "a"
##  [4951] "c" "g" "g" "g" "g" "g" "c" "g" "a" "c" "c" "c" "c" "t" "a" "a" "a" "a"
##  [4969] "c" "g" "t" "g" "a" "a" "g" "a" "g" "g" "g" "a" "g" "c" "g" "g" "t" "a"
##  [4987] "a" "a" "a" "a" "g" "t" "a" "a" "c" "t" "g" "c" "a" "c" "t" "c" "a" "a"
##  [5005] "g" "g" "g" "c" "t" "g" "c" "g" "t" "g" "g" "g" "a" "t" "a" "a" "g" "t"
##  [5023] "c" "c" "t" "t" "g" "g" "a" "a" "c" "c" "g" "a" "g" "c" "c" "a" "t" "g"
##  [5041] "g" "a" "c" "t" "c" "g" "c" "c" "a" "t" "c" "g" "a" "a" "a" "g" "g" "g"
##  [5059] "c" "g" "a" "c" "t" "t" "a" "g" "c" "a" "a" "t" "t" "t" "a" "a" "a" "t"
##  [5077] "a" "g" "c" "c" "t" "a" "c" "g" "c" "g" "a" "g" "c" "g" "g" "g" "t" "c"
##  [5095] "c" "g" "a" "c" "g" "a" "g" "t" "a" "a" "c" "g" "g" "t" "a" "c" "g" "g"
##  [5113] "g" "g" "g" "a" "g" "a" "a" "c" "c" "g" "c" "t" "a" "a" "g" "t" "t" "c"
##  [5131] "c" "c" "c" "a" "a" "a" "a" "a" "t" "t" "c" "c" "g" "t" "c" "t" "c" "g"
##  [5149] "t" "t" "t" "c" "c" "g" "a" "g" "g" "g" "a" "a" "a" "g" "g" "g" "a" "c"
##  [5167] "c" "c" "g" "c" "g" "g" "c" "t" "g" "t" "a" "a" "g" "t" "a" "c" "g" "t"
##  [5185] "t" "a" "g" "c" "t" "g" "g" "c" "t" "g" "g" "c" "c" "c" "a" "c" "a" "g"
##  [5203] "g" "g" "g" "c" "a" "g" "t" "a" "t" "a" "g" "t" "t" "c" "g" "t" "g" "c"
##  [5221] "c" "t" "t" "a" "a" "c" "a" "t" "t" "g" "g" "t" "c" "g" "a" "c" "c" "a"
##  [5239] "a" "a" "a" "t" "c" "a" "a" "a" "t" "g" "a" "a" "t" "t" "t" "a" "c" "t"
##  [5257] "a" "a" "c" "g" "a" "a" "g" "c" "g" "t" "g" "g" "g" "c" "t" "g" "a" "t"
##  [5275] "t" "a" "t" "g" "t" "g" "c" "a" "a" "c" "c" "a" "a" "c" "g" "g" "t" "c"
##  [5293] "g" "g" "a" "g" "t" "c" "c" "t" "a" "c" "c" "g" "g" "t" "a" "a" "c" "t"
##  [5311] "c" "g" "g" "g" "t" "g" "g" "c" "t" "g" "t" "c" "g" "a" "g" "g" "g" "g"
##  [5329] "c" "a" "c" "c" "a" "g" "a" "a" "a" "t" "c" "t" "g" "a" "g" "g" "a" "g"
##  [5347] "c" "g" "g" "c" "a" "c" "t" "t" "c" "c" "t" "t" "a" "g" "a" "t" "g" "a"
##  [5365] "g" "a" "g" "g" "g" "g" "a" "t" "t" "g" "g" "g" "c" "c" "g" "t" "t" "g"
##  [5383] "g" "c" "g" "g" "t" "t" "t" "c" "t" "g" "g" "c" "a" "g" "a" "a" "a" "g"
##  [5401] "g" "g" "g" "t" "a" "g" "g" "c" "t" "a" "c" "a" "g" "c" "g" "t" "c" "a"
##  [5419] "a" "c" "t" "g" "g" "g" "t" "g" "g" "a" "a" "c" "g" "t" "a" "c" "c" "g"
##  [5437] "c" "c" "t" "g" "a" "c" "g" "a" "c" "t" "a" "a" "t" "a" "t" "c" "c" "g"
##  [5455] "a" "a" "c" "a" "c" "c" "g" "c" "g" "c" "c" "c" "c" "t" "a" "a" "a" "c"
##  [5473] "a" "a" "g" "t" "c" "g" "g" "c" "a" "a" "g" "g" "t" "a" "g" "c" "c" "g"
##  [5491] "a" "c" "c" "g" "c" "t" "a" "g" "a" "t" "g" "g" "g" "t" "g" "g" "a" "g"
##  [5509] "a" "g" "g" "t" "c" "a" "g" "g" "a" "c" "c" "c" "g" "t" "t" "c" "a" "g"
##  [5527] "a" "g" "g" "t" "g" "c" "c" "t" "g" "a" "c" "c" "t" "a" "c" "c" "g" "a"
##  [5545] "t" "t" "t" "t" "c" "g" "a" "g" "c" "c" "g" "c" "c" "a" "g" "g" "g" "a"
##  [5563] "g" "t" "g" "c" "g" "g" "c" "a" "c" "a" "t" "g" "c" "g" "a" "a" "t" "g"
##  [5581] "a" "t" "c" "t" "g" "g" "g" "a" "c" "c" "t" "g" "g" "t" "c" "c" "g" "g"
##  [5599] "g" "a" "t" "g" "g" "t" "t" "c" "t" "a" "a" "t" "c" "a" "g" "g" "g" "g"
##  [5617] "g" "a" "c" "g" "a" "g" "a" "t" "c" "t" "a" "c" "g" "g" "g" "c" "a" "g"
##  [5635] "a" "a" "a" "c" "a" "t" "g" "t" "g" "a" "c" "c" "t" "g" "t" "a" "g" "t"
##  [5653] "c" "g" "a" "t" "g" "g" "a" "c" "t" "g" "a" "a" "g" "t" "c" "a" "c" "c"
##  [5671] "g" "g" "a" "c" "a" "c" "g" "g" "a" "g" "c" "a" "g" "t" "c" "a" "c" "g"
##  [5689] "g" "t" "c" "a" "c" "c" "g" "c" "g" "c" "t" "g" "g" "c" "g" "t" "a" "c"
##  [5707] "g" "c" "g" "a" "g" "g" "g" "t" "a" "a" "g" "c" "g" "a" "a" "c" "t" "t"
##  [5725] "g" "a" "a" "a" "g" "a" "t" "a" "c" "g" "a" "c" "c" "c" "t" "t" "t" "a"
##  [5743] "g" "t" "g" "g" "g" "c" "g" "g" "t" "t" "a" "c" "c" "g" "g" "g" "a" "g"
##  [5761] "c" "c" "a" "g" "c" "t" "g" "t" "a" "g" "a" "g" "a" "c" "a" "c" "g" "c"
##  [5779] "g" "c" "a" "t" "g" "a" "t" "a" "a" "c" "t" "g" "a" "a" "g" "g" "g" "a"
##  [5797] "a" "c" "t" "t" "t" "c" "c" "a" "a" "c" "a" "g" "g" "c" "g" "c" "a" "g"
##  [5815] "g" "t" "g" "g" "c" "a" "g" "g" "g" "g" "g" "t" "a" "a" "t" "g" "t" "t"
##  [5833] "a" "g" "a" "g" "c" "g" "t" "c" "g" "g" "t" "a" "g" "a" "t" "c" "g" "g"
##  [5851] "c" "c" "c" "c" "c" "a" "t" "g" "g" "a" "g" "a" "c" "c" "g" "g" "g" "g"
##  [5869] "t" "c" "t" "a" "g" "g" "t" "t" "a" "g" "g" "c" "t" "g" "a" "g" "c" "g"
##  [5887] "g" "a" "c" "a" "c" "g" "g" "c" "t" "a" "c" "g" "t" "c" "a" "g" "c" "c"
##  [5905] "t" "a" "t" "a" "a" "c" "c" "c" "t" "c" "c" "a" "g" "c" "a" "c" "t" "t"
##  [5923] "g" "c" "a" "t" "c" "a" "t" "a" "c" "a" "a" "t" "t" "t" "c" "a" "g" "c"
##  [5941] "t" "g" "a" "a" "g" "a" "a" "t" "t" "t" "g" "a" "c" "c" "g" "c" "a" "a"
##  [5959] "a" "g" "g" "a" "a" "g" "g" "g" "t" "a" "a" "t" "c" "t" "g" "c" "g" "g"
##  [5977] "c" "g" "a" "c" "a" "g" "g" "g" "c" "g" "t" "t" "t" "a" "a" "g" "a" "t"
##  [5995] "a" "c" "a" "t" "a" "t" "g" "a" "g" "t" "g" "a" "a" "a" "t" "g" "t" "c"
##  [6013] "c" "c" "c" "a" "a" "c" "t" "g" "c" "a" "t" "g" "t" "c" "t" "a" "a" "c"
##  [6031] "a" "g" "g" "c" "a" "g" "c" "a" "g" "t" "g" "g" "g" "c" "c" "g" "t" "g"
##  [6049] "t" "t" "a" "g" "g" "a" "t" "t" "t" "g" "g" "c" "a" "g" "t" "c" "g" "g"
##  [6067] "c" "g" "a" "g" "a" "c" "a" "g" "g" "t" "c" "g" "c" "g" "a" "c" "c" "g"
##  [6085] "t" "c" "c" "t" "t" "c" "g" "c" "t" "c" "t" "g" "g" "g" "c" "c" "t" "c"
##  [6103] "t" "c" "c" "t" "g" "g" "g" "t" "g" "c" "g" "a" "t" "a" "c" "g" "c" "a"
##  [6121] "g" "c" "a" "a" "c" "t" "g" "g" "g" "c" "c" "c" "t" "g" "a" "a" "g" "c"
##  [6139] "g" "t" "c" "g" "a" "a" "c" "g" "c" "a" "c" "g" "g" "a" "g" "a" "g" "c"
##  [6157] "t" "c" "c" "a" "a" "g" "g" "g" "a" "c" "c" "g" "c" "a" "t" "c" "a" "a"
##  [6175] "g" "c" "a" "c" "a" "t" "c" "g" "a" "a" "c" "g" "c" "g" "c" "a" "c" "a"
##  [6193] "c" "g" "c" "g" "g" "t" "g" "g" "t" "c" "t" "a" "c" "c" "c" "g" "t" "c"
##  [6211] "a" "a" "t" "t" "g" "g" "c" "a" "a" "a" "c" "c" "a" "a" "t" "t" "a" "t"
##  [6229] "t" "t" "a" "a" "t" "g" "t" "c" "g" "g" "a" "c" "g" "t" "c" "c" "g" "a"
##  [6247] "g" "t" "c" "g" "g" "g" "g" "t" "g" "g" "c" "a" "a" "g" "c" "a" "g" "a"
##  [6265] "a" "g" "g" "c" "g" "g" "g" "a" "a" "a" "t" "g" "a" "g" "t" "t" "a" "g"
##  [6283] "g" "c" "a" "a" "a" "g" "a" "a" "g" "g" "a" "t" "g" "t" "g" "g" "c" "c"
##  [6301] "g" "g" "a" "c" "g" "g" "a" "g" "g" "a" "a" "a" "g" "t" "g" "c" "a" "t"
##  [6319] "c" "c" "g" "t" "c" "a" "c" "a" "g" "c" "g" "a" "g" "a" "a" "c" "a" "a"
##  [6337] "t" "t" "g" "g" "a" "a" "g" "g" "g" "a" "c" "t" "g" "a" "g" "c" "a" "a"
##  [6355] "g" "a" "c" "g" "a" "a" "g" "a" "g" "g" "c" "a" "a" "g" "g" "g" "a" "a"
##  [6373] "g" "a" "c" "t" "t" "g" "g" "t" "a" "t" "g" "t" "c" "g" "a" "g" "g" "c"
##  [6391] "a" "g" "g" "a" "g" "g" "a" "c" "t" "g" "g" "t" "g" "c" "g" "g" "g" "c"
##  [6409] "g" "c" "t" "g" "a" "a" "c" "t" "a" "g" "c" "a" "t" "c" "a" "g" "c" "g"
##  [6427] "g" "t" "a" "c" "g" "t" "a" "c" "t" "c" "g" "c" "g" "g" "a" "t" "a" "g"
##  [6445] "g" "t" "c" "g" "c" "a" "t" "a" "c" "g" "t" "t" "a" "g" "c" "g" "a" "g"
##  [6463] "c" "c" "c" "g" "c" "t" "a" "a" "t" "c" "c" "t" "g" "a" "c" "t" "c" "c"
##  [6481] "c" "a" "c" "a" "c" "c" "a" "a" "g" "g" "g" "a" "g" "c" "t" "c" "t" "a"
##  [6499] "a" "t" "g" "g" "a" "a" "c" "a" "g" "c" "c" "a" "t" "a" "g" "t" "a" "g"
##  [6517] "g" "g" "g" "a" "g" "c" "g" "a" "a" "t" "c" "a" "c" "g" "c" "c" "c" "t"
##  [6535] "g" "g" "a" "t" "a" "g" "a" "g" "c" "a" "t" "t" "g" "c" "c" "t" "g" "g"
##  [6553] "a" "g" "c" "g" "g" "c" "a" "a" "a" "g" "a" "g" "c" "g" "a" "a" "g" "g"
##  [6571] "a" "t" "t" "g" "g" "g" "t" "c" "t" "t" "t" "a" "c" "a" "a" "g" "g" "a"
##  [6589] "c" "t" "c" "g" "a" "a" "a" "c" "g" "c" "a" "t" "g" "t" "c" "g" "a" "g"
##  [6607] "c" "t" "a" "t" "c" "c" "a" "g" "g" "a" "t" "g" "g" "g" "c" "a" "c" "a"
##  [6625] "g" "t" "a" "c" "g" "c" "g" "c" "g" "a" "c" "g" "g" "c" "t" "a" "c" "t"
##  [6643] "g" "c" "c" "a" "g" "c" "t" "a" "g" "g" "a" "c" "a" "g" "t" "g" "t" "a"
##  [6661] "t" "g" "a" "a" "g" "a" "g" "g" "g" "g" "c" "t" "c" "g" "g" "t" "c" "t"
##  [6679] "t" "t" "t" "g" "c" "c" "a" "g" "c" "g" "g" "g" "c" "g" "c" "c" "g" "c"
##  [6697] "a" "a" "c" "c" "a" "t" "a" "g" "t" "t" "a" "g" "g" "g" "g" "g" "c" "g"
##  [6715] "g" "a" "g" "g" "g" "a" "a" "c" "a" "g" "a" "c" "g" "g" "g" "g" "g" "a"
##  [6733] "c" "g" "g" "g" "t" "a" "a" "a" "t" "a" "c" "a" "t" "g" "a" "t" "g" "c"
##  [6751] "a" "g" "g" "t" "t" "t" "a" "a" "a" "a" "a" "g" "a" "g" "g" "a" "c" "g"
##  [6769] "g" "t" "g" "g" "t" "a" "c" "g" "c" "a" "t" "t" "g" "t" "c" "a" "t" "a"
##  [6787] "g" "t" "c" "a" "t" "g" "c" "c" "t" "g" "t" "t" "c" "t" "c" "a" "a" "c"
##  [6805] "g" "g" "t" "c" "c" "g" "a" "a" "g" "c" "g" "t" "a" "c" "g" "c" "t" "c"
##  [6823] "a" "c" "c" "g" "t" "c" "g" "g" "c" "a" "a" "c" "g" "c" "g" "a" "t" "a"
##  [6841] "g" "t" "g" "c" "g" "a" "a" "t" "g" "a" "c" "a" "t" "a" "g" "a" "g" "t"
##  [6859] "t" "a" "c" "t" "t" "a" "a" "g" "t" "c" "c" "c" "t" "c" "a" "c" "g" "a"
##  [6877] "a" "g" "g" "c" "c" "c" "c" "g" "c" "t" "g" "t" "t" "g" "g" "g" "t" "c"
##  [6895] "c" "t" "t" "g" "g" "g" "g" "t" "a" "g" "g" "g" "g" "t" "g" "c" "g" "a"
##  [6913] "c" "g" "c" "c" "t" "a" "g" "c" "g" "a" "a" "g" "g" "c" "g" "c" "g" "c"
##  [6931] "g" "t" "a" "g" "a" "g" "t" "t" "a" "a" "g" "a" "a" "g" "a" "g" "g" "c"
##  [6949] "g" "c" "g" "t" "t" "t" "g" "c" "a" "t" "a" "t" "a" "c" "a" "t" "c" "c"
##  [6967] "g" "a" "g" "g" "c" "a" "a" "t" "g" "t" "c" "g" "g" "t" "g" "c" "a" "a"
##  [6985] "c" "g" "c" "t" "c" "g" "g" "g" "a" "c" "t" "t" "a" "g" "g" "c" "g" "a"
##  [7003] "g" "t" "g" "g" "g" "g" "a" "c" "t" "a" "t" "g" "g" "c" "g" "t" "a" "t"
##  [7021] "g" "c" "a" "c" "g" "c" "c" "a" "g" "t" "t" "a" "t" "a" "g" "g" "c" "a"
##  [7039] "c" "g" "c" "g" "g" "a" "a" "t" "a" "c" "t" "a" "c" "g" "g" "a" "t" "g"
##  [7057] "a" "a" "a" "g" "c" "a" "g" "g" "g" "c" "c" "c" "t" "t" "g" "t" "c" "a"
##  [7075] "c" "a" "a" "g" "g" "t" "c" "c" "a" "a" "a" "c" "a" "c" "c" "c" "c" "c"
##  [7093] "g" "c" "a" "t" "c" "a" "g" "c" "t" "t" "g" "g" "g" "t" "g" "a" "t" "a"
##  [7111] "g" "t" "g" "t" "g" "t" "t" "a" "g" "a" "c" "g" "a" "g" "g" "g" "g" "a"
##  [7129] "a" "t" "c" "c" "a" "g" "t" "a" "c" "a" "c" "t" "g" "a" "g" "g" "g" "g"
##  [7147] "a" "g" "g" "c" "g" "c" "t" "g" "g" "a" "t" "g" "c" "c" "g" "a" "c" "c"
##  [7165] "t" "t" "g" "a" "g" "g" "a" "g" "t" "c" "g" "g" "a" "c" "c" "a" "c" "c"
##  [7183] "g" "c" "t" "c" "c" "t" "t" "c" "a" "g" "a" "g" "c" "t" "g" "a" "t" "g"
##  [7201] "g" "g" "g" "t" "a" "g" "c" "c" "a" "a" "t" "g" "g" "g" "t" "t" "c" "g"
##  [7219] "a" "g" "g" "c" "g" "a" "g" "g" "t" "c" "g" "c" "g" "a" "a" "c" "g" "a"
##  [7237] "t" "t" "g" "c" "t" "g" "c" "c" "t" "g" "a" "t" "g" "c" "g" "t" "a" "a"
##  [7255] "c" "t" "t" "a" "a" "t" "g" "t" "c" "c" "c" "c" "g" "t" "c" "g" "g" "a"
##  [7273] "a" "a" "c" "c" "c" "g" "c" "g" "g" "g" "g" "c" "c" "g" "g" "a" "g" "a"
##  [7291] "g" "a" "t" "a" "c" "c" "g" "t" "g" "g" "a" "g" "t" "g" "a" "t" "c" "g"
##  [7309] "g" "a" "a" "c" "t" "g" "c" "g" "c" "c" "c" "c" "g" "g" "c" "t" "t" "g"
##  [7327] "t" "c" "c" "c" "c" "c" "g" "c" "t" "a" "g" "a" "t" "t" "g" "c" "g" "a"
##  [7345] "g" "c" "c" "a" "g" "g" "a" "t" "c" "g" "c" "t" "c" "g" "t" "c" "g" "a"
##  [7363] "g" "a" "g" "g" "t" "g" "g" "t" "t" "a" "c" "g" "t" "g" "g" "g" "c" "g"
##  [7381] "a" "c" "t" "t" "a" "t" "a" "g" "g" "g" "c" "c" "t" "c" "g" "t" "c" "c"
##  [7399] "t" "t" "t" "t" "t" "c" "a" "a" "g" "c" "c" "c" "a" "a" "c" "a" "t" "g"
##  [7417] "a" "c" "t" "g" "t" "g" "a" "a" "a" "a" "t" "a" "a" "g" "c" "g" "t" "g"
##  [7435] "a" "t" "t" "t" "a" "g" "t" "c" "a" "g" "g" "c" "c" "a" "t" "c" "t" "a"
##  [7453] "g" "g" "a" "a" "c" "a" "g" "c" "t" "c" "a" "g" "a" "a" "t" "a" "c" "c"
##  [7471] "g" "g" "t" "a" "c" "t" "a" "t" "a" "c" "a" "t" "g" "a" "g" "c" "a" "c"
##  [7489] "g" "a" "c" "t" "c" "t" "t" "c" "t" "a" "c" "c" "t" "c" "t" "a" "t" "g"
##  [7507] "g" "c" "c" "t" "t" "a" "g" "g" "g" "a" "g" "t" "g" "a" "c" "c" "a" "t"
##  [7525] "g" "t" "g" "c" "t" "g" "a" "c" "g" "g" "c" "c" "t" "g" "c" "a" "t" "a"
##  [7543] "c" "a" "g" "g" "a" "c" "g" "c" "g" "a" "t" "g" "c" "c" "t" "g" "t" "a"
##  [7561] "t" "c" "c" "g" "a" "c" "a" "a" "c" "c" "g" "t" "g" "g" "g" "t" "c" "t"
##  [7579] "a" "a" "t" "c" "t" "t" "t" "c" "t" "c" "c" "t" "g" "c" "g" "g" "g" "a"
##  [7597] "a" "t" "g" "t" "a" "g" "g" "c" "c" "a" "t" "g" "t" "a" "g" "g" "g" "g"
##  [7615] "t" "a" "g" "t" "c" "a" "c" "t" "g" "c" "a" "a" "g" "c" "g" "a" "a" "a"
##  [7633] "a" "g" "c" "g" "g" "c" "a" "a" "c" "g" "c" "g" "a" "c" "g" "t" "c" "g"
##  [7651] "a" "g" "t" "a" "t" "g" "g" "c" "g" "g" "t" "c" "g" "a" "g" "c" "a" "a"
##  [7669] "c" "c" "t" "g" "c" "a" "g" "a" "g" "c" "a" "g" "c" "g" "t" "a" "g" "a"
##  [7687] "c" "c" "c" "t" "a" "a" "c" "a" "c" "g" "a" "c" "t" "g" "t" "t" "t" "a"
##  [7705] "c" "t" "t" "a" "a" "g" "t" "c" "g" "c" "g" "g" "g" "t" "t" "a" "g" "g"
##  [7723] "g" "a" "t" "g" "g" "g" "t" "t" "a" "t" "a" "c" "a" "g" "a" "a" "a" "a"
##  [7741] "a" "t" "t" "g" "g" "a" "a" "g" "g" "t" "t" "g" "a" "g" "a" "t" "t" "c"
##  [7759] "c" "a" "t" "a" "c" "g" "a" "t" "c" "g" "g" "a" "g" "g" "c" "t" "g" "c"
##  [7777] "g" "c" "g" "a" "a" "a" "g" "c" "t" "t" "g" "t" "c" "g" "g" "g" "g" "t"
##  [7795] "c" "t" "c" "g" "g" "g" "a" "g" "g" "t" "t" "t" "c" "t" "g" "a" "g" "a"
##  [7813] "c" "t" "g" "g" "c" "a" "g" "g" "t" "t" "a" "c" "c" "c" "c" "a" "c" "g"
##  [7831] "a" "g" "a" "t" "c" "g" "g" "a" "a" "a" "t" "g" "a" "a" "t" "g" "a" "a"
##  [7849] "c" "c" "c" "g" "g" "a" "a" "t" "g" "t" "a" "a" "g" "a" "c" "a" "a" "c"
##  [7867] "g" "c" "c" "c" "c" "c" "c" "g" "t" "c" "g" "c" "c" "a" "g" "a" "a" "t"
##  [7885] "t" "g" "a" "a" "g" "a" "g" "t" "g" "c" "a" "c" "a" "a" "c" "c" "g" "g"
##  [7903] "c" "c" "t" "c" "g" "t" "a" "t" "c" "c" "g" "c" "a" "a" "t" "c" "a" "c"
##  [7921] "t" "a" "c" "t" "t" "c" "g" "c" "t" "g" "t" "a" "c" "a" "c" "c" "t" "c"
##  [7939] "g" "c" "t" "g" "a" "c" "g" "a" "a" "a" "a" "a" "c" "g" "c" "c" "t" "a"
##  [7957] "a" "a" "a" "g" "g" "c" "a" "a" "g" "g" "t" "g" "c" "a" "g" "a" "t" "c"
##  [7975] "g" "c" "a" "a" "a" "t" "t" "a" "a" "g" "a" "c" "a" "a" "t" "t" "c" "t"
##  [7993] "a" "a" "g" "a" "c" "t" "a" "c" "t" "t" "g" "a" "a" "t" "g" "t" "t" "g"
##  [8011] "g" "g" "g" "c" "c" "g" "t" "c" "t" "t" "c" "c" "a" "t" "g" "t" "g" "a"
##  [8029] "g" "a" "g" "a" "t" "g" "c" "g" "a" "g" "c" "a" "g" "g" "a" "g" "g" "g"
##  [8047] "g" "c" "g" "c" "c" "g" "g" "t" "g" "g" "a" "g" "c" "t" "c" "a" "t" "g"
##  [8065] "g" "c" "g" "a" "g" "g" "a" "a" "g" "a" "g" "c" "a" "a" "t" "c" "c" "a"
##  [8083] "t" "a" "t" "c" "t" "a" "a" "c" "t" "g" "t" "c" "g" "t" "a" "a" "g" "c"
##  [8101] "g" "a" "c" "t" "g" "c" "g" "c" "t" "g" "t" "t" "t" "c" "g" "g" "t" "a"
##  [8119] "a" "g" "c" "c" "a" "g" "g" "c" "a" "t" "c" "t" "g" "c" "a" "a" "c" "g"
##  [8137] "c" "c" "g" "c" "a" "g" "a" "c" "t" "t" "c" "t" "a" "t" "c" "g" "c" "c"
##  [8155] "c" "c" "c" "t" "a" "g" "c" "g" "t" "a" "g" "a" "c" "g" "c" "c" "a" "g"
##  [8173] "c" "a" "g" "a" "g" "g" "a" "c" "c" "c" "a" "t" "t" "g" "t" "a" "a" "g"
##  [8191] "g" "c" "c" "g" "a" "g" "t" "c" "c" "a" "g" "t" "g" "g" "g" "a" "g" "g"
##  [8209] "g" "c" "g" "c" "t" "c" "c" "t" "g" "a" "a" "t" "g" "g" "t" "g" "c" "t"
##  [8227] "a" "g" "c" "a" "g" "g" "t" "t" "g" "a" "g" "c" "a" "a" "c" "c" "c" "c"
##  [8245] "g" "t" "g" "g" "g" "c" "c" "a" "a" "t" "a" "a" "g" "a" "c" "t" "c" "a"
##  [8263] "g" "c" "g" "c" "a" "t" "c" "c" "a" "a" "g" "t" "t" "c" "g" "t" "g" "g"
##  [8281] "t" "a" "t" "a" "g" "g" "a" "c" "g" "a" "c" "t" "g" "a" "g" "g" "c" "a"
##  [8299] "c" "c" "c" "c" "g" "c" "c" "c" "a" "g" "c" "a" "g" "a" "g" "a" "t" "g"
##  [8317] "a" "a" "a" "t" "g" "t" "c" "g" "a" "g" "t" "t" "c" "c" "c" "c" "a" "a"
##  [8335] "g" "a" "t" "c" "g" "c" "a" "a" "t" "c" "a" "a" "c" "a" "a" "g" "g" "g"
##  [8353] "g" "g" "t" "g" "a" "a" "c" "g" "g" "a" "a" "g" "a" "a" "a" "t" "c" "t"
##  [8371] "a" "a" "g" "g" "c" "g" "g" "g" "c" "g" "a" "t" "a" "a" "a" "a" "t" "g"
##  [8389] "g" "c" "c" "c" "t" "a" "c" "g" "c" "g" "a" "g" "g" "a" "a" "a" "t" "t"
##  [8407] "a" "t" "g" "t" "g" "c" "g" "a" "t" "c" "c" "t" "t" "t" "t" "a" "c" "a"
##  [8425] "c" "c" "c" "c" "g" "a" "c" "a" "a" "g" "g" "c" "t" "c" "a" "c" "g" "a"
##  [8443] "c" "t" "c" "c" "c" "a" "a" "a" "a" "t" "a" "a" "g" "a" "t" "g" "c" "g"
##  [8461] "g" "g" "g" "a" "a" "t" "c" "c" "a" "c" "a" "a" "a" "c" "g" "g" "t" "a"
##  [8479] "g" "t" "g" "g" "c" "a" "g" "c" "g" "t" "g" "a" "t" "c" "a" "a" "g" "c"
##  [8497] "g" "t" "a" "g" "t" "t" "t" "g" "g" "a" "a" "a" "a" "a" "g" "c" "c" "g"
##  [8515] "g" "t" "c" "t" "a" "t" "t" "t" "g" "t" "g" "c" "a" "c" "c" "t" "c" "c"
##  [8533] "a" "g" "t" "c" "a" "g" "c" "a" "c" "c" "t" "c" "c" "g" "a" "t" "a" "g"
##  [8551] "a" "c" "g" "c" "g" "a" "g" "a" "c" "t" "c" "g" "g" "c" "a" "a" "g" "a"
##  [8569] "g" "a" "g" "c" "g" "t" "c" "a" "a" "a" "g" "t" "a" "g" "c" "c" "a" "t"
##  [8587] "c" "g" "t" "c" "g" "c" "g" "g" "t" "c" "a" "a" "g" "a" "c" "c" "g" "g"
##  [8605] "t" "a" "g" "g" "a" "g" "t" "g" "t" "c" "c" "a" "g" "t" "g" "c" "g" "c"
##  [8623] "c" "g" "g" "c" "t" "c" "a" "c" "c" "a" "g" "c" "c" "c" "c" "a" "t" "g"
##  [8641] "g" "g" "a" "g" "g" "t" "a" "t" "t" "c" "t" "c" "g" "c" "g" "a" "t" "g"
##  [8659] "g" "a" "a" "g" "a" "g" "g" "g" "g" "c" "c" "a" "g" "g" "g" "g" "g" "c"
##  [8677] "a" "t" "c" "t" "g" "t" "a" "g" "c" "t" "g" "t" "t" "c" "t" "c" "a" "c"
##  [8695] "g" "a" "a" "t" "g" "g" "g" "g" "a" "g" "c" "g" "a" "a" "g" "c" "g" "g"
##  [8713] "t" "a" "a" "c" "g" "c" "t" "a" "a" "a" "t" "g" "g" "g" "t" "c" "a" "t"
##  [8731] "g" "g" "a" "t" "g" "t" "c" "t" "a" "g" "a" "t" "g" "c" "c" "a" "g" "g"
##  [8749] "g" "c" "a" "g" "g" "t" "a" "g" "g" "g" "g" "c" "a" "c" "c" "t" "a" "g"
##  [8767] "t" "g" "a" "c" "t" "t" "g" "a" "g" "a" "t" "g" "t" "g" "g" "t" "c" "t"
##  [8785] "a" "t" "a" "a" "c" "c" "c" "g" "g" "c" "a" "t" "g" "c" "c" "a" "g" "c"
##  [8803] "c" "g" "c" "t" "t" "t" "t" "g" "t" "a" "g" "t" "a" "t" "g" "a" "g" "a"
##  [8821] "a" "a" "g" "t" "c" "c" "g" "a" "g" "g" "c" "a" "t" "c" "c" "c" "g" "g"
##  [8839] "a" "g" "c" "g" "t" "a" "t" "t" "g" "a" "t" "g" "c" "t" "a" "g" "t" "g"
##  [8857] "t" "t" "t" "t" "t" "c" "t" "t" "c" "a" "g" "g" "t" "a" "a" "a" "a" "c"
##  [8875] "c" "c" "a" "a" "a" "c" "a" "a" "g" "a" "a" "t" "c" "g" "t" "a" "c" "a"
##  [8893] "g" "c" "c" "g" "t" "c" "g" "c" "c" "a" "a" "g" "c" "a" "c" "t" "t" "a"
##  [8911] "g" "a" "a" "t" "t" "c" "g" "a" "c" "g" "a" "g" "g" "t" "g" "g" "a" "t"
##  [8929] "c" "g" "t" "c" "c" "t" "a" "a" "c" "t" "a" "c" "a" "a" "g" "g" "t" "g"
##  [8947] "t" "g" "a" "g" "c" "g" "c" "a" "g" "t" "c" "a" "g" "c" "c" "c" "a" "a"
##  [8965] "g" "c" "c" "t" "a" "t" "g" "t" "a" "c" "c" "c" "t" "t" "t" "g" "g" "c"
##  [8983] "c" "t" "g" "t" "c" "c" "a" "c" "a" "t" "g" "g" "a" "a" "a" "t" "a" "g"
##  [9001] "c" "g" "a" "c" "t" "c" "t" "g" "a" "t" "c" "g" "g" "c" "t" "g" "a" "c"
##  [9019] "a" "a" "g" "g" "a" "t" "c" "c" "t" "c" "c" "c" "c" "g" "a" "t" "g" "g"
##  [9037] "c" "g" "g" "a" "t" "g" "c" "a" "t" "a" "a" "a" "g" "t" "t" "c" "t" "g"
##  [9055] "c" "t" "a" "g" "g" "a" "t" "c" "a" "g" "g" "c" "g" "c" "g" "g" "c" "a"
##  [9073] "c" "a" "a" "g" "g" "t" "g" "g" "c" "a" "a" "t" "a" "g" "g" "t" "c" "t"
##  [9091] "t" "c" "g" "c" "c" "g" "a" "c" "c" "a" "t" "c" "g" "g" "g" "c" "g" "g"
##  [9109] "t" "a" "t" "c" "c" "c" "g" "a" "t" "g" "c" "c" "t" "a" "c" "c" "g" "g"
##  [9127] "t" "g" "t" "a" "a" "c" "a" "g" "g" "t" "g" "g" "c" "a" "t" "a" "c" "g"
##  [9145] "a" "g" "a" "a" "g" "c" "g" "t" "a" "g" "c" "g" "c" "a" "t" "a" "t" "a"
##  [9163] "g" "a" "g" "g" "c" "a" "a" "c" "a" "c" "g" "g" "t" "g" "g" "t" "g" "c"
##  [9181] "g" "t" "g" "a" "c" "c" "a" "c" "c" "t" "a" "a" "c" "g" "c" "c" "g" "t"
##  [9199] "a" "a" "t" "g" "a" "a" "g" "c" "g" "g" "c" "c" "g" "g" "t" "t" "a" "g"
##  [9217] "t" "a" "g" "a" "g" "c" "t" "g" "t" "a" "g" "g" "c" "t" "t" "t" "t" "t"
##  [9235] "g" "g" "g" "a" "c" "a" "c" "c" "a" "a" "a" "g" "g" "a" "t" "g" "g" "g"
##  [9253] "a" "a" "a" "g" "g" "g" "a" "a" "a" "a" "a" "g" "a" "c" "a" "g" "a" "a"
##  [9271] "c" "g" "a" "t" "a" "a" "c" "g" "g" "g" "a" "a" "t" "g" "g" "t" "c" "c"
##  [9289] "a" "c" "a" "g" "t" "t" "a" "t" "a" "t" "c" "c" "g" "g" "a" "a" "g" "t"
##  [9307] "c" "c" "g" "c" "t" "c" "a" "g" "g" "g" "t" "a" "g" "c" "c" "a" "t" "c"
##  [9325] "t" "g" "c" "c" "g" "c" "g" "a" "a" "g" "a" "c" "t" "g" "t" "c" "a" "g"
##  [9343] "g" "g" "t" "a" "g" "a" "g" "a" "c" "a" "g" "g" "t" "a" "t" "g" "t" "g"
##  [9361] "g" "t" "g" "c" "g" "g" "g" "a" "c" "t" "t" "g" "c" "c" "t" "a" "t" "a"
##  [9379] "c" "c" "g" "t" "t" "g" "c" "g" "a" "t" "a" "a" "g" "c" "t" "t" "g" "g"
##  [9397] "a" "a" "a" "t" "a" "a" "a" "a" "t" "a" "a" "t" "t" "g" "g" "a" "c" "g"
##  [9415] "c" "t" "c" "g" "g" "g" "t" "g" "a" "a" "g" "a" "c" "a" "a" "g" "g" "g"
##  [9433] "g" "c" "a" "c" "a" "a" "g" "g" "g" "c" "a" "a" "g" "g" "g" "t" "c" "a"
##  [9451] "t" "c" "g" "a" "g" "g" "c" "g" "t" "c" "c" "g" "c" "g" "c" "g" "c" "t"
##  [9469] "g" "g" "g" "t" "a" "g" "c" "g" "g" "c" "g" "c" "g" "a" "a" "a" "c" "t"
##  [9487] "g" "a" "t" "c" "g" "g" "g" "t" "c" "c" "c" "t" "c" "c" "g" "c" "c" "g"
##  [9505] "c" "c" "g" "c" "g" "a" "c" "g" "t" "a" "t" "g" "g" "c" "g" "g" "c" "t"
##  [9523] "t" "c" "t" "g" "g" "g" "c" "g" "c" "g" "t" "a" "c" "g" "a" "a" "t" "g"
##  [9541] "g" "c" "g" "c" "c" "t" "c" "t" "a" "c" "c" "t" "a" "g" "t" "g" "g" "g"
##  [9559] "g" "g" "g" "c" "g" "t" "a" "c" "t" "c" "g" "a" "a" "g" "a" "g" "t" "g"
##  [9577] "c" "t" "a" "c" "g" "g" "a" "a" "c" "t" "t" "g" "a" "t" "a" "g" "g" "t"
##  [9595] "a" "t" "g" "a" "c" "t" "a" "g" "g" "t" "c" "c" "c" "a" "a" "g" "c" "g"
##  [9613] "a" "t" "g" "t" "g" "g" "a" "a" "c" "g" "t" "t" "a" "a" "a" "c" "t" "t"
##  [9631] "g" "c" "t" "g" "a" "t" "g" "a" "c" "g" "t" "a" "a" "g" "g" "g" "a" "g"
##  [9649] "c" "t" "g" "a" "g" "c" "g" "t" "c" "g" "c" "g" "c" "a" "a" "a" "t" "a"
##  [9667] "g" "c" "c" "t" "g" "c" "t" "g" "c" "t" "a" "t" "c" "c" "c" "c" "g" "c"
##  [9685] "g" "c" "a" "c" "a" "c" "a" "t" "a" "g" "t" "t" "a" "t" "g" "t" "a" "c"
##  [9703] "a" "g" "a" "g" "g" "g" "a" "g" "t" "g" "t" "g" "g" "g" "c" "g" "c" "a"
##  [9721] "g" "c" "a" "g" "g" "c" "t" "g" "c" "c" "c" "t" "t" "c" "g" "c" "c" "g"
##  [9739] "g" "g" "t" "a" "a" "g" "t" "c" "c" "c" "a" "t" "t" "a" "t" "g" "g" "c"
##  [9757] "t" "g" "a" "a" "c" "a" "g" "g" "c" "a" "a" "a" "a" "g" "c" "g" "a" "c"
##  [9775] "t" "g" "g" "t" "t" "c" "g" "c" "g" "t" "t" "a" "g" "c" "t" "a" "c" "c"
##  [9793] "g" "c" "c" "c" "a" "c" "a" "t" "t" "a" "c" "t" "g" "t" "c" "c" "a" "t"
##  [9811] "a" "a" "c" "g" "c" "a" "a" "c" "g" "c" "c" "c" "g" "a" "c" "t" "t" "g"
##  [9829] "a" "g" "g" "a" "g" "c" "t" "a" "a" "g" "g" "g" "c" "a" "t" "g" "a" "g"
##  [9847] "t" "c" "c" "g" "a" "g" "g" "a" "c" "t" "t" "g" "a" "g" "c" "g" "a" "g"
##  [9865] "t" "g" "g" "c" "g" "t" "g" "a" "a" "t" "g" "c" "t" "g" "t" "a" "g" "a"
##  [9883] "t" "c" "a" "g" "c" "g" "t" "g" "g" "g" "a" "g" "c" "a" "a" "t" "g" "g"
##  [9901] "g" "g" "g" "g" "t" "g" "c" "t" "g" "c" "c" "c" "a" "c" "g" "c" "c" "g"
##  [9919] "c" "a" "g" "g" "c" "c" "a" "c" "c" "c" "t" "a" "a" "a" "g" "c" "c" "g"
##  [9937] "t" "g" "t" "g" "a" "c" "g" "c" "a" "c" "t" "c" "t" "t" "g" "t" "g" "t"
##  [9955] "a" "g" "g" "c" "g" "g" "a" "g" "t" "c" "t" "a" "c" "t" "c" "t" "c" "a"
##  [9973] "t" "a" "t" "g" "g" "g" "g" "t" "g" "a" "t" "t" "g" "g" "g" "a" "c" "a"
##  [9991] "g" "g" "t" "t" "g" "c" "g" "t" "c" "g" "t" "c" "c" "g" "a" "t" "t" "a"
## [10009] "a" "c" "t" "g" "c" "c" "c" "a" "t" "a" "c" "g" "g" "g" "t" "a" "c" "g"
## [10027] "c" "a" "g" "c" "g" "c" "a" "a" "c" "a" "t" "a" "g" "g" "t" "a" "c" "g"
## [10045] "a" "t" "g" "t" "g" "t" "c" "g" "c" "a" "g" "c" "g" "g" "a" "t" "g" "t"
## [10063] "g" "a" "a" "c" "g" "g" "c" "g" "t" "g" "t" "t" "c" "c" "a" "g" "c" "a"
## [10081] "c" "g" "a" "a" "a" "a" "c" "c" "t" "g" "t" "g" "t" "g" "c" "c" "a" "c"
## [10099] "t" "g" "c" "t" "g" "c" "g" "g" "t" "c" "c" "c" "a" "c" "a" "a" "g" "g"
## [10117] "g" "a" "t" "a" "c" "g" "g" "a" "g" "a" "c" "t" "c" "a" "g" "a" "c" "a"
## [10135] "c" "a" "c" "a" "c" "g" "g" "a" "g" "a" "g" "c" "t" "t" "g" "t" "g" "a"
## [10153] "g" "g" "g" "c" "a" "a" "g" "c" "c" "a" "a" "a" "c" "t" "a" "c" "t" "t"
## [10171] "g" "g" "g" "g" "c" "c" "a" "c" "g" "g" "a" "g" "a" "a" "a" "t" "a" "g"
## [10189] "g" "a" "t" "a" "t" "a" "g" "a" "a" "a" "a" "c" "g" "g" "t" "c" "g" "c"
## [10207] "a" "a" "a" "g" "g" "a" "a" "g" "t" "g" "g" "t" "a" "g" "g" "c" "c" "a"
## [10225] "t" "g" "a" "g" "g" "g" "c" "a" "c" "g" "g" "a" "g" "a" "g" "c" "a" "t"
## [10243] "c" "c" "t" "g" "c" "g" "t" "t" "c" "c" "c" "c" "c" "c" "t" "a" "g" "a"
## [10261] "a" "t" "c" "a" "c" "a" "c" "g" "a" "c" "g" "g" "a" "a" "g" "t" "t" "g"
## [10279] "c" "t" "a" "g" "c" "t" "c" "a" "g" "a" "g" "t" "t" "g" "t" "t" "a" "g"
## [10297] "a" "c" "g" "a" "a" "g" "t" "g" "t" "c" "c" "g" "a" "a" "c" "t" "c" "c"
## [10315] "g" "g" "t" "c" "g" "a" "a" "t" "g" "a" "a" "g" "a" "g" "a" "g" "a" "g"
## [10333] "g" "g" "c" "g" "c" "g" "g" "g" "a" "g" "a" "a" "a" "t" "a" "t" "t" "a"
## [10351] "c" "g" "c" "c" "t" "g" "g" "t" "g" "c" "t" "g" "a" "t" "g" "g" "g" "t"
## [10369] "t" "c" "g" "g" "c" "g" "c" "a" "a" "g" "g" "a" "g" "g" "a" "c" "g" "a"
## [10387] "t" "c" "c" "c" "c" "c" "a" "g" "g" "c" "a" "t" "c" "c" "a" "t" "c" "g"
## [10405] "t" "g" "g" "g" "c" "g" "g" "g" "c" "c" "a" "a" "g" "a" "g" "g" "a" "t"
## [10423] "c" "a" "a" "a" "t" "g" "c" "c" "g" "g" "c" "t" "g" "g" "c" "c" "c" "a"
## [10441] "c" "g" "g" "c" "t" "c" "t" "c" "a" "c" "g" "t" "a" "a" "a" "a" "t" "t"
## [10459] "t" "c" "a" "c" "g" "g" "a" "c" "t" "c" "c" "g" "g" "t" "c" "c" "g" "a"
## [10477] "g" "t" "t" "g" "g" "c" "g" "a" "c" "g" "c" "t" "a" "c" "c" "c" "a" "g"
## [10495] "a" "g" "a" "a" "a" "g" "t" "g" "g" "t" "t" "t" "c" "g" "g" "a" "t" "g"
## [10513] "g" "t" "a" "t" "a" "c" "a" "g" "g" "a" "a" "t" "c" "g" "a" "c" "g" "g"
## [10531] "g" "g" "g" "a" "a" "a" "g" "g" "a" "g" "c" "a" "g" "a" "t" "g" "a" "c"
## [10549] "t" "g" "t" "c" "t" "c" "t" "g" "t" "g" "g" "g" "g" "a" "g" "g" "a" "a"
## [10567] "g" "a" "c" "a" "g" "c" "g" "g" "a" "a" "c" "g" "g" "a" "c" "a" "t" "c"
## [10585] "g" "g" "c" "a" "a" "g" "a" "t" "t" "g" "t" "t" "a" "a" "a" "c" "g" "g"
## [10603] "c" "a" "g" "c" "a" "a" "t" "t" "g" "g" "a" "a" "a" "c" "a" "g" "t" "a"
## [10621] "c" "t" "t" "a" "g" "g" "a" "c" "c" "g" "c" "g" "t" "c" "g" "a" "g" "g"
## [10639] "c" "a" "a" "t" "c" "a" "g" "c" "t" "t" "g" "a" "g" "t" "g" "t" "c" "g"
## [10657] "t" "t" "t" "c" "c" "t" "g" "g" "g" "g" "g" "a" "c" "t" "c" "a" "g" "c"
## [10675] "a" "g" "a" "a" "g" "t" "t" "c" "c" "t" "g" "a" "a" "t" "a" "a" "g" "g"
## [10693] "a" "g" "c" "t" "a" "a" "g" "g" "g" "c" "c" "t" "a" "t" "t" "g" "c" "g"
## [10711] "c" "a" "c" "g" "c" "a" "a" "a" "g" "g" "a" "g" "c" "t" "g" "t" "c" "t"
## [10729] "g" "t" "t" "c" "c" "c" "g" "c" "g" "g" "g" "t" "t" "g" "a" "a" "a" "a"
## [10747] "c" "g" "a" "g" "t" "c" "g" "a" "g" "c" "a" "g" "g" "t" "a" "c" "t" "g"
## [10765] "a" "t" "c" "g" "g" "a" "g" "g" "a" "g" "t" "g" "a" "g" "g" "g" "a" "g"
## [10783] "a" "c" "c" "g" "c" "c" "a" "t" "g" "t" "t" "c" "c" "c" "a" "t" "g" "c"
## [10801] "g" "c" "a" "c" "c" "c" "c" "c" "t" "g" "t" "c" "a" "c" "a" "g" "a" "c"
## [10819] "g" "t" "g" "g" "c" "c" "g" "a" "t" "a" "t" "t" "a" "a" "g" "g" "g" "a"
## [10837] "t" "g" "c" "a" "g" "g" "a" "c" "a" "a" "a" "g" "t" "a" "c" "g" "c" "c"
## [10855] "g" "g" "c" "g" "g" "a" "a" "a" "t" "g" "c" "a" "c" "g" "c" "c" "c" "g"
## [10873] "a" "a" "t" "g" "t" "a" "g" "g" "t" "g" "a" "c" "a" "c" "c" "c" "c" "g"
## [10891] "a" "g" "a" "c" "c" "g" "c" "g" "g" "g" "t" "g" "g" "c" "t" "g" "a" "a"
## [10909] "c" "g" "c" "g" "a" "a" "g" "g" "t" "a" "t" "t" "t" "g" "g" "a" "t" "c"
## [10927] "c" "a" "c" "g" "c" "t" "t" "g" "g" "g" "a" "c" "a" "g" "g" "g" "t" "c"
## [10945] "g" "g" "g" "g" "c" "t" "g" "g" "a" "c" "g" "c" "g" "c" "g" "t" "c" "a"
## [10963] "t" "t" "c" "t" "t" "t" "t" "g" "g" "c" "a" "a" "t" "g" "c" "g" "t" "c"
## [10981] "c" "t" "g" "a" "c" "g" "t" "c" "c" "c" "c" "a" "g" "c" "a" "t" "a" "g"
## [10999] "t" "c" "c" "g" "a" "c" "c" "c" "c" "c" "a" "g" "g" "g" "t" "a" "g" "g"
## [11017] "g" "a" "a" "g" "a" "t" "a" "g" "g" "g" "c" "g" "c" "g" "g" "t" "a" "a"
## [11035] "c" "a" "g" "g" "c" "g" "c" "a" "g" "c" "c" "c" "t" "t" "c" "c" "a" "t"
## [11053] "c" "t" "a" "g" "g" "g" "t" "c" "t" "t" "t" "c" "t" "a" "c" "a" "g" "g"
## [11071] "c" "g" "c" "t" "c" "a" "a" "t" "t" "g" "g" "c" "t" "a" "a" "c" "c" "a"
## [11089] "a" "g" "c" "g" "g" "c" "g" "t" "g" "g" "a" "t" "g" "a" "g" "c" "c" "g"
## [11107] "c" "t" "g" "c" "c" "t" "a" "g" "t" "t" "c" "g" "c" "c" "g" "a" "a" "a"
## [11125] "t" "a" "g" "g" "a" "c" "g" "a" "c" "a" "c" "a" "g" "g" "a" "g" "g" "c"
## [11143] "g" "c" "t" "g" "c" "c" "a" "t" "a" "a" "g" "g" "g" "g" "t" "a" "a" "a"
## [11161] "g" "c" "t" "g" "g" "c" "g" "c" "t" "g" "g" "c" "a" "c" "t" "g" "a" "a"
## [11179] "c" "g" "g" "g" "g" "c" "g" "g" "t" "a" "g" "c" "a" "a" "c" "g" "g" "t"
## [11197] "g" "g" "g" "c" "t" "g" "g" "c" "t" "t" "g" "a" "c" "g" "t" "c" "c" "c"
## [11215] "a" "c" "t" "t" "t" "c" "c" "a" "g" "c" "t" "c" "g" "t" "g" "t" "a" "g"
## [11233] "c" "t" "c" "c" "t" "c" "a" "a" "c" "c" "a" "c" "t" "c" "a" "a" "g" "a"
## [11251] "t" "g" "a" "a" "c" "a" "a" "t" "g" "a" "a" "t" "t" "c" "c" "c" "g" "a"
## [11269] "t" "a" "g" "g" "t" "c" "c" "t" "a" "g" "t" "a" "t" "a" "c" "g" "g" "c"
## [11287] "c" "g" "t" "a" "g" "t" "c" "g" "t" "a" "c" "c" "t" "c" "t" "g" "g" "a"
## [11305] "g" "t" "t" "g" "a" "g" "g" "c" "c" "c" "a" "t" "c" "c" "g" "g" "c" "t"
## [11323] "c" "t" "a" "a" "a" "c" "a" "g" "a" "t" "t" "g" "g" "g" "c" "g" "g" "t"
## [11341] "a" "t" "t" "a" "g" "t" "a" "a" "t" "t" "g" "a" "g" "c" "g" "t" "c" "t"
## [11359] "g" "c" "a" "c" "g" "t" "g" "g" "a" "t" "a" "c" "g" "a" "t" "t" "t" "t"
## [11377] "g" "g" "c" "a" "g" "a" "a" "g" "t" "c" "a" "a" "t" "t" "t" "a" "a" "g"
## [11395] "t" "g" "g" "c" "g" "a" "g" "a" "c" "c" "g" "c" "g" "a" "g" "c" "c" "t"
## [11413] "a" "g" "a" "t" "a" "t" "t" "t" "c" "g" "t" "g" "a" "g" "g" "t" "g" "a"
## [11431] "g" "a" "a" "a" "a" "g" "a" "a" "a" "g" "t" "t" "c" "a" "g" "g" "c" "g"
## [11449] "a" "g" "c" "g" "c" "g" "g" "g" "a" "t" "t" "c" "c" "a" "g" "t" "g" "g"
## [11467] "a" "g" "a" "a" "g" "c" "a" "a" "c" "a" "t" "c" "a" "a" "g" "a" "g" "g"
## [11485] "a" "g" "a" "g" "g" "t" "a" "g" "a" "c" "c" "a" "t" "t" "g" "c" "a" "g"
## [11503] "t" "a" "g" "g" "a" "t" "c" "g" "g" "c" "a" "c" "t" "g" "c" "g" "a" "a"
## [11521] "g" "c" "a" "t" "t" "t" "a" "c" "t" "g" "g" "a" "t" "a" "t" "a" "t" "g"
## [11539] "a" "t" "a" "t" "a" "c" "g" "a" "a" "c" "c" "g" "c" "g" "c" "t" "a" "c"
## [11557] "c" "g" "c" "t" "g" "t" "t" "t" "t" "a" "t" "t" "g" "t" "c" "g" "g" "g"
## [11575] "g" "c" "c" "a" "t" "a" "a" "t" "c" "c" "a" "a" "a" "a" "c" "a" "a" "g"
## [11593] "c" "a" "a" "g" "g" "g" "a" "t" "a" "g" "t" "c" "t" "g" "t" "t" "t" "t"
## [11611] "a" "g" "g" "t" "c" "g" "a" "a" "c" "a" "t" "g" "c" "g" "a" "a" "g" "c"
## [11629] "c" "g" "g" "g" "c" "g" "a" "c" "c" "c" "g" "g" "g" "c" "c" "a" "t" "c"
## [11647] "a" "a" "g" "a" "g" "t" "a" "t" "a" "g" "a" "t" "a" "c" "c" "a" "a" "a"
## [11665] "t" "g" "c" "c" "a" "c" "c" "a" "t" "t" "a" "a" "c" "a" "g" "c" "g" "c"
## [11683] "g" "g" "a" "t" "c" "t" "g" "a" "c" "a" "g" "g" "c" "c" "a" "a" "c" "g"
## [11701] "g" "a" "t" "a" "g" "g" "c" "t" "t" "g" "a" "c" "t" "a" "c" "a" "a" "t"
## [11719] "g" "c" "a" "a" "a" "g" "g" "g" "a" "t" "a" "c" "g" "g" "g" "a" "t" "c"
## [11737] "a" "a" "g" "a" "a" "a" "t" "a" "t" "g" "a" "t" "c" "a" "a" "c" "t" "c"
## [11755] "g" "a" "c" "a" "g" "c" "g" "t" "a" "c" "c" "t" "g" "t" "a" "t" "a" "t"
## [11773] "a" "g" "a" "t" "t" "g" "c" "c" "t" "g" "c" "c" "t" "g" "t" "c" "g" "t"
## [11791] "t" "t" "g" "g" "g" "a" "a" "c" "c" "t" "t" "c" "a" "g" "g" "a" "t" "a"
## [11809] "a" "g" "t" "g" "g" "a" "g" "a" "a" "a" "g" "a" "a" "a" "g" "a" "c" "t"
## [11827] "a" "g" "t" "c" "g" "c" "c" "a" "a" "a" "a" "g" "t" "c" "g" "c" "t" "c"
## [11845] "g" "c" "c" "a" "a" "g" "a" "a" "g" "c" "c" "t" "a" "c" "t" "g" "g" "a"
## [11863] "c" "c" "t" "a" "t" "a" "g" "t" "t" "a" "a" "a" "a" "t" "a" "c" "g" "g"
## [11881] "g" "g" "g" "t" "a" "c" "g" "c" "a" "g" "c" "t" "g" "g" "a" "g" "c" "c"
## [11899] "g" "a" "a" "c" "a" "c" "t" "g" "g" "t" "t" "t" "a" "g" "g" "g" "g" "c"
## [11917] "c" "c" "g" "a" "t" "g" "t" "c" "c" "g" "g" "a" "g" "c" "t" "t" "t" "a"
## [11935] "g" "c" "a" "c" "a" "g" "c" "a" "a" "g" "t" "a" "c" "a" "t" "a" "a" "t"
## [11953] "g" "c" "g" "c" "g" "g" "g" "c" "c" "c" "g" "a" "t" "g" "a" "t" "c" "a"
## [11971] "a" "g" "t" "g" "c" "c" "g" "g" "a" "c" "t" "g" "c" "t" "g" "g" "g" "a"
## [11989] "g" "a" "t" "g" "c" "a" "g" "c" "t" "c" "t" "c" "g" "t" "c" "g" "g" "t"
## [12007] "a" "g" "a" "c" "g" "a" "t" "t" "c" "t" "t" "g" "g" "a" "a" "a" "g" "a"
## [12025] "t" "g" "a" "a" "a" "g" "c" "g" "a" "c" "a" "c" "t" "a" "c" "g" "c" "g"
## [12043] "t" "c" "a" "c" "c" "c" "a" "a" "a" "g" "g" "c" "c" "t" "a" "t" "t" "c"
## [12061] "c" "a" "g" "a" "a" "g" "t" "c" "g" "a" "c" "c" "t" "a" "g" "t" "g" "a"
## [12079] "g" "g" "t" "t" "a" "g" "g" "g" "c" "c" "c" "g" "t" "c" "c" "g" "a" "g"
## [12097] "c" "a" "a" "a" "g" "t" "t" "g" "c" "a" "a" "a" "c" "c" "c" "t" "g" "c"
## [12115] "t" "g" "t" "t" "a" "c" "g" "a" "a" "g" "a" "t" "c" "g" "t" "g" "c" "a"
## [12133] "a" "c" "a" "g" "t" "g" "a" "t" "t" "t" "t" "g" "g" "a" "g" "g" "g" "c"
## [12151] "a" "c" "t" "a" "t" "a" "g" "g" "c" "c" "a" "g" "a" "a" "c" "a" "a" "c"
## [12169] "g" "g" "c" "c" "g" "a" "t" "g" "g" "c" "a" "c" "g" "a" "t" "g" "g" "a"
## [12187] "g" "a" "c" "c" "t" "a" "g" "g" "a" "a" "c" "g" "g" "g" "a" "c" "g" "g"
## [12205] "a" "c" "c" "t" "t" "c" "g" "c" "g" "a" "a" "a" "c" "a" "t" "c" "g" "a"
## [12223] "c" "c" "t" "g" "t" "t" "a" "a" "a" "c" "c" "c" "c" "a" "a" "t" "a" "g"
## [12241] "a" "a" "g" "t" "a" "t" "t" "c" "a" "t" "g" "c" "g" "t" "g" "t" "t" "g"
## [12259] "g" "c" "a" "g" "a" "g" "c" "g" "g" "a" "a" "a" "c" "c" "a" "c" "g" "t"
## [12277] "c" "a" "c" "g" "g" "c" "c" "g" "c" "c" "t" "c" "g" "g" "g" "g" "g" "a"
## [12295] "a" "a" "a" "a" "g" "c" "g" "t" "a" "c" "t" "g" "g" "g" "c" "t" "c" "g"
## [12313] "c" "a" "t" "a" "g" "g" "t" "g" "g" "g" "c" "g" "t" "g" "a" "g" "t" "a"
## [12331] "t" "t" "c" "g" "g" "a" "g" "g" "a" "c" "g" "a" "c" "g" "t" "c" "g" "a"
## [12349] "t" "c" "g" "g" "a" "a" "c" "t" "a" "t" "t" "t" "g" "g" "t" "g" "a" "c"
## [12367] "a" "c" "g" "t" "t" "t" "c" "a" "t" "g" "c" "g" "g" "a" "c" "c" "t" "a"
## [12385] "c" "a" "a" "t" "a" "t" "g" "t" "a" "a" "g" "g" "a" "g" "g" "a" "t" "g"
## [12403] "a" "g" "a" "a" "t" "g" "t" "g" "a" "g" "a" "g" "g" "g" "t" "t" "c" "a"
## [12421] "t" "g" "g" "a" "a" "a" "g" "a" "c" "g" "t" "t" "c" "a" "t" "g" "c" "g"
## [12439] "g" "c" "g" "c" "a" "a" "t" "a" "a" "a" "c" "a" "g" "g" "t" "c" "t" "g"
## [12457] "c" "a" "c" "g" "a" "a" "c" "g" "a" "a" "a" "t" "g" "c" "a" "a" "t" "a"
## [12475] "a" "c" "c" "a" "c" "t" "t" "c" "c" "t" "a" "a" "g" "c" "g" "a" "c" "a"
## [12493] "g" "c" "a" "t" "c" "g" "a" "a" "t" "c" "g" "c" "a" "t" "a" "c" "t" "g"
## [12511] "t" "c" "a" "g" "t" "g" "a" "g" "t" "g" "g" "c" "g" "g" "t" "c" "c" "t"
## [12529] "g" "t" "t" "a" "t" "g" "c" "c" "t" "a" "t" "a" "t" "a" "a" "a" "g" "c"
## [12547] "c" "t" "g" "t" "a" "a" "g" "c" "g" "g" "a" "g" "a" "t" "c" "g" "g" "g"
## [12565] "t" "g" "a" "a" "t" "c" "t" "g" "g" "a" "g" "g" "g" "c" "t" "a" "g" "c"
## [12583] "a" "a" "a" "t" "t" "a" "g" "a" "g" "a" "c" "g" "g" "c" "a" "c" "c" "c"
## [12601] "t" "a" "a" "c" "a" "c" "c" "g" "a" "c" "t" "g" "a" "t" "c" "t" "a" "c"
## [12619] "g" "g" "c" "g" "t" "c" "t" "t" "t" "c" "a" "c" "c" "c" "g" "g" "a" "a"
## [12637] "t" "c" "g" "c" "g" "t" "c" "t" "t" "g" "a" "c" "g" "a" "g" "t" "t" "g"
## [12655] "c" "g" "c" "a" "c" "t" "c" "g" "a" "g" "t" "g" "c" "g" "a" "t" "g" "c"
## [12673] "c" "g" "c" "t" "c" "c" "a" "c" "c" "t" "t" "a" "a" "t" "c" "c" "a" "g"
## [12691] "t" "t" "g" "c" "a" "g" "t" "g" "a" "c" "g" "c" "g" "t" "g" "c" "g" "g"
## [12709] "g" "g" "t" "c" "t" "g" "g" "g" "a" "t" "g" "t" "t" "c" "t" "g" "g" "c"
## [12727] "g" "a" "g" "g" "t" "t" "c" "t" "c" "g" "c" "a" "g" "c" "t" "t" "c" "c"
## [12745] "a" "g" "g" "a" "g" "a" "g" "a" "a" "c" "t" "g" "t" "c" "g" "a" "t" "g"
## [12763] "c" "t" "g" "a" "c" "g" "t" "c" "a" "a" "g" "g" "c" "a" "g" "c" "a" "c"
## [12781] "a" "g" "c" "a" "a" "g" "g" "a" "c" "a" "c" "a" "g" "c" "c" "g" "g" "g"
## [12799] "a" "g" "g" "a" "g" "g" "c" "t" "g" "t" "t" "c" "c" "a" "g" "a" "g" "g"
## [12817] "a" "c" "t" "g" "g" "a" "g" "g" "c" "t" "t" "g" "g" "a" "g" "a" "g" "t"
## [12835] "g" "g" "a" "c" "g" "g" "t" "c" "g" "g" "c" "g" "a" "c" "g" "g" "c" "g"
## [12853] "t" "g" "a" "t" "c" "g" "g" "g" "t" "a" "g" "c" "a" "t" "t" "g" "c" "t"
## [12871] "g" "t" "a" "c" "t" "g" "g" "c" "a" "c" "t" "g" "g" "a" "g" "g" "g" "g"
## [12889] "a" "a" "g" "g" "t" "a" "t" "t" "g" "g" "c" "c" "t" "a" "g" "a" "t" "a"
## [12907] "t" "a" "a" "a" "g" "g" "g" "a" "t" "g" "t" "a" "t" "t" "a" "a" "a" "g"
## [12925] "a" "g" "g" "c" "g" "a" "g" "t" "g" "g" "t" "a" "a" "t" "c" "a" "c" "t"
## [12943] "c" "g" "t" "g" "c" "c" "a" "t" "a" "a" "g" "t" "c" "g" "g" "g" "t" "t"
## [12961] "g" "t" "g" "g" "a" "a" "c" "g" "g" "c" "c" "c" "g" "c" "a" "g" "a" "a"
## [12979] "c" "g" "c" "a" "a" "t" "a" "g" "a" "a" "c" "g" "g" "g" "c" "c" "g" "c"
## [12997] "a" "c" "t" "g" "a" "c" "t" "g" "a" "g" "a" "g" "a" "g" "g" "c" "c" "g"
## [13015] "g" "g" "t" "c" "g" "g" "g" "g" "g" "c" "g" "a" "a" "c" "g" "g" "g" "a"
## [13033] "t" "t" "c" "c" "c" "t" "g" "t" "t" "c" "a" "g" "t" "a" "c" "a" "a" "c"
## [13051] "g" "g" "g" "g" "c" "c" "c" "g" "g" "g" "g" "t" "a" "g" "t" "g" "c" "a"
## [13069] "a" "c" "t" "t" "t" "c" "g" "t" "a" "g" "g" "t" "a" "c" "t" "a" "a" "a"
## [13087] "g" "g" "t" "a" "a" "a" "g" "g" "t" "g" "a" "a" "a" "g" "t" "c" "t" "g"
## [13105] "g" "t" "a" "c" "c" "a" "g" "a" "g" "c" "g" "t" "g" "g" "c" "c" "g" "g"
## [13123] "g" "g" "a" "c" "g" "c" "t" "t" "t" "t" "a" "g" "a" "a" "g" "g" "g" "g"
## [13141] "g" "g" "a" "a" "a" "a" "g" "g" "g" "c" "a" "t" "g" "t" "a" "c" "a" "c"
## [13159] "g" "g" "a" "a" "c" "a" "t" "c" "a" "t" "t" "t" "g" "a" "g" "g" "c" "g"
## [13177] "a" "g" "c" "g" "g" "c" "a" "a" "t" "c" "t" "g" "c" "a" "a" "t" "a" "g"
## [13195] "a" "c" "g" "c" "c" "c" "a" "t" "c" "c" "c" "a" "t" "a" "a" "g" "c" "c"
## [13213] "a" "t" "g" "c" "c" "c" "t" "g" "g" "c" "c" "c" "a" "c" "a" "a" "g" "g"
## [13231] "c" "g" "a" "t" "g" "c" "g" "a" "a" "t" "g" "c" "a" "a" "a" "c" "a" "g"
## [13249] "a" "t" "a" "a" "c" "a" "t" "c" "g" "c" "g" "c" "g" "g" "c" "c" "a" "a"
## [13267] "t" "a" "g" "t" "c" "g" "c" "c" "g" "g" "c" "a" "a" "g" "t" "c" "t" "g"
## [13285] "c" "c" "t" "t" "g" "a" "c" "g" "t" "t" "a" "t" "g" "c" "g" "c" "g" "g"
## [13303] "t" "g" "g" "a" "t" "c" "a" "c" "a" "t" "g" "c" "a" "t" "g" "g" "t" "a"
## [13321] "g" "t" "g" "a" "g" "c" "c" "a" "c" "g" "g" "g" "c" "t" "c" "t" "a" "c"
## [13339] "a" "g" "c" "g" "g" "a" "g" "t" "a" "c" "c" "a" "g" "c" "a" "g" "g" "a"
## [13357] "a" "c" "a" "c" "a" "g" "t" "c" "a" "a" "g" "a" "g" "t" "g" "t" "t" "t"
## [13375] "t" "c" "g" "t" "a" "g" "t" "c" "g" "g" "c" "t" "t" "a" "t" "a" "g" "g"
## [13393] "a" "t" "t" "a" "g" "t" "c" "c" "t" "a" "a" "g" "t" "c" "a" "t" "c" "a"
## [13411] "c" "t" "c" "a" "t" "t" "c" "g" "t" "t" "t" "t" "c" "g" "t" "c" "a" "g"
## [13429] "a" "t" "a" "c" "c" "c" "g" "a" "g" "g" "c" "a" "a" "t" "t" "g" "t" "a"
## [13447] "a" "c" "t" "g" "t" "g" "t" "c" "t" "a" "a" "g" "a" "c" "t" "c" "g" "g"
## [13465] "a" "g" "t" "t" "a" "g" "g" "a" "a" "t" "t" "c" "t" "t" "c" "g" "t" "a"
## [13483] "a" "g" "g" "g" "c" "g" "a" "c" "t" "g" "a" "a" "g" "g" "a" "a" "g" "a"
## [13501] "t" "c" "a" "t" "t" "t" "a" "c" "a" "a" "g" "a" "a" "c" "a" "a" "a" "a"
## [13519] "a" "t" "g" "t" "t" "c" "g" "t" "g" "a" "c" "g" "c" "c" "c" "a" "t" "a"
## [13537] "t" "g" "t" "c" "c" "c" "g" "g" "g" "c" "c" "t" "a" "g" "g" "a" "g" "a"
## [13555] "g" "g" "g" "a" "c" "t" "c" "a" "a" "g" "c" "t" "g" "c" "a" "c" "c" "a"
## [13573] "t" "c" "g" "c" "a" "g" "a" "c" "c" "a" "a" "a" "g" "g" "t" "a" "g" "c"
## [13591] "g" "t" "t" "c" "g" "c" "t" "t" "a" "t" "g" "g" "t" "a" "t" "c" "g" "c"
## [13609] "g" "t" "g" "t" "c" "t" "a" "g" "g" "a" "g" "t" "g" "c" "t" "a" "a" "g"
## [13627] "c" "g" "c" "c" "c" "a" "c" "c" "a" "a" "t" "t" "a" "t" "c" "g" "a" "a"
## [13645] "a" "t" "a" "c" "c" "g" "c" "g" "a" "g" "g" "g" "t" "g" "g" "g" "g" "c"
## [13663] "a" "c" "t" "g" "c" "g" "c" "t" "g" "t" "c" "c" "t" "c" "a" "g" "g" "c"
## [13681] "g" "a" "a" "a" "g" "g" "t" "g" "t" "g" "c" "g" "a" "c" "g" "a" "g" "a"
## [13699] "c" "a" "g" "t" "g" "a" "a" "a" "g" "c" "c" "a" "t" "a" "t" "g" "g" "c"
## [13717] "a" "a" "c" "a" "g" "a" "c" "a" "c" "c" "a" "c" "a" "t" "g" "t" "g" "g"
## [13735] "g" "c" "c" "g" "g" "a" "a" "a" "g" "g" "g" "a" "a" "g" "c" "c" "g" "t"
## [13753] "g" "g" "g" "g" "c" "g" "a" "c" "g" "t" "g" "a" "t" "t" "c" "c" "g" "a"
## [13771] "g" "c" "a" "a" "t" "g" "a" "t" "a" "a" "t" "c" "a" "t" "g" "t" "g" "g"
## [13789] "c" "g" "g" "g" "c" "a" "g" "c" "a" "g" "a" "a" "g" "a" "g" "g" "g" "c"
## [13807] "g" "c" "t" "a" "a" "g" "g" "g" "a" "a" "c" "c" "g" "a" "g" "c" "t" "a"
## [13825] "t" "t" "c" "a" "g" "g" "g" "g" "t" "g" "g" "c" "g" "t" "g" "t" "g" "a"
## [13843] "t" "t" "c" "c" "c" "a" "g" "a" "a" "g" "g" "g" "g" "t" "g" "t" "g" "a"
## [13861] "g" "c" "a" "a" "g" "a" "t" "t" "a" "t" "g" "a" "c" "a" "g" "g" "g" "a"
## [13879] "a" "a" "a" "t" "a" "c" "a" "c" "a" "a" "g" "t" "a" "t" "t" "g" "a" "a"
## [13897] "c" "g" "a" "t" "a" "t" "c" "c" "g" "c" "c" "g" "a" "c" "a" "g" "g" "c"
## [13915] "t" "a" "a" "t" "t" "c" "c" "g" "a" "g" "c" "g" "a" "g" "t" "c" "g" "a"
## [13933] "g" "a" "a" "t" "g" "a" "g" "g" "c" "t" "c" "c" "a" "g" "g" "a" "g" "g"
## [13951] "a" "t" "g" "t" "c" "g" "a" "c" "c" "a" "a" "a" "a" "t" "g" "a" "c" "g"
## [13969] "a" "a" "t" "t" "c" "g" "g" "c" "a" "g" "g" "g" "g" "a" "a" "t" "c" "g"
## [13987] "a" "c" "g" "g" "g" "t" "a" "g" "a" "g" "g" "g" "g" "c" "t" "a" "g" "a"
## [14005] "t" "c" "g" "a" "a" "t" "t" "c" "g" "a" "t" "g" "g" "c" "g" "c" "t" "c"
## [14023] "a" "g" "c" "g" "t" "t" "t" "c" "a" "a" "g" "t" "g" "a" "a" "t" "c" "t"
## [14041] "c" "t" "g" "t" "g" "a" "a" "t" "c" "t" "c" "c" "g" "t" "t" "a" "a" "t"
## [14059] "g" "c" "a" "c" "c" "t" "a" "c" "g" "g" "t" "g" "c" "g" "a" "g" "a" "c"
## [14077] "g" "a" "t" "a" "g" "a" "a" "g" "t" "c" "c" "g" "c" "c" "t" "a" "a" "a"
## [14095] "t" "a" "t" "g" "c" "a" "t" "c" "g" "t" "g" "t" "g" "t" "g" "g" "g" "g"
## [14113] "a" "t" "t" "t" "a" "c" "c" "c" "t" "c" "a" "g" "t" "a" "t" "c" "c" "t"
## [14131] "a" "t" "g" "c" "a" "c" "g" "t" "a" "c" "a" "a" "c" "a" "c" "c" "a" "c"
## [14149] "c" "c" "g" "t" "c" "a" "g" "a" "g" "t" "t" "a" "t" "a" "a" "a" "a" "t"
## [14167] "c" "g" "g" "g" "a" "g" "a" "t" "a" "a" "t" "t" "t" "g" "t" "g" "t" "a"
## [14185] "c" "g" "a" "g" "c" "c" "t" "g" "t" "g" "c" "a" "g" "a" "a" "t" "c" "c"
## [14203] "a" "c" "g" "a" "t" "g" "a" "g" "t" "g" "g" "c" "a" "g" "g" "c" "t" "a"
## [14221] "c" "a" "g" "a" "g" "t" "c" "g" "g" "c" "a" "t" "c" "g" "a" "c" "a" "g"
## [14239] "a" "t" "a" "g" "g" "a" "a" "g" "a" "a" "t" "g" "t" "a" "g" "g" "a" "a"
## [14257] "t" "g" "g" "a" "a" "t" "g" "a" "a" "c" "g" "a" "c" "t" "t" "t" "a" "t"
## [14275] "c" "c" "a" "t" "a" "a" "g" "c" "g" "g" "g" "t" "a" "t" "g" "c" "t" "c"
## [14293] "g" "a" "g" "t" "t" "g" "c" "c" "t" "t" "a" "g" "a" "a" "g" "c" "t" "c"
## [14311] "g" "t" "c" "c" "t" "t" "g" "g" "g" "a" "g" "g" "t" "c" "t" "c" "a" "a"
## [14329] "g" "c" "c" "a" "c" "c" "a" "c" "c" "a" "g" "g" "c" "g" "a" "g" "t" "c"
## [14347] "g" "a" "g" "a" "c" "g" "a" "g" "g" "a" "c" "a" "t" "g" "g" "g" "a" "a"
## [14365] "g" "t" "g" "t" "c" "c" "c" "c" "c" "g" "c" "g" "g" "a" "a" "c" "c" "c"
## [14383] "c" "g" "t" "c" "t" "g" "a" "t" "g" "g" "g" "c" "g" "t" "c" "a" "g" "g"
## [14401] "t" "a" "c" "t" "g" "t" "c" "c" "g" "c" "t" "a" "g" "g" "a" "g" "c" "t"
## [14419] "t" "c" "g" "g" "c" "a" "a" "c" "t" "a" "t" "g" "t" "c" "c" "a" "c" "c"
## [14437] "t" "a" "g" "g" "g" "g" "g" "a" "c" "a" "a" "a" "c" "t" "t" "g" "g" "g"
## [14455] "a" "a" "c" "g" "t" "a" "g" "c" "t" "c" "t" "a" "t" "t" "g" "t" "g" "g"
## [14473] "t" "g" "t" "c" "t" "g" "g" "a" "a" "g" "t" "c" "t" "g" "g" "c" "c" "c"
## [14491] "g" "a" "a" "a" "c" "a" "g" "a" "a" "c" "c" "a" "g" "c" "a" "t" "t" "a"
## [14509] "g" "a" "t" "c" "g" "c" "a" "g" "a" "c" "t" "t" "c" "g" "t" "c" "g" "c"
## [14527] "a" "a" "a" "a" "g" "a" "t" "c" "g" "g" "t" "t" "g" "c" "c" "t" "c" "t"
## [14545] "g" "t" "t" "c" "a" "a" "c" "c" "g" "t" "c" "c" "c" "t" "a" "c" "t" "g"
## [14563] "a" "g" "t" "c" "t" "t" "g" "g" "t" "t" "g" "c" "a" "c" "g" "c" "g" "c"
## [14581] "t" "t" "g" "a" "a" "t" "t" "a" "g" "a" "a" "t" "a" "c" "g" "t" "t" "t"
## [14599] "c" "c" "g" "c" "a" "c" "g" "a" "t" "c" "a" "c" "g" "g" "a" "g" "a" "g"
## [14617] "g" "a" "g" "g" "t" "c" "c" "t" "a" "a" "t" "a" "c" "g" "t" "a" "c" "g"
## [14635] "g" "c" "c" "g" "c" "c" "t" "c" "g" "c" "t" "c" "c" "a" "g" "g" "t" "c"
## [14653] "g" "c" "g" "g" "c" "c" "c" "g" "g" "t" "g" "a" "a" "t" "g" "g" "g" "a"
## [14671] "a" "g" "a" "t" "a" "c" "t" "g" "g" "g" "a" "g" "t" "g" "c" "t" "c" "g"
## [14689] "t" "t" "c" "g" "g" "t" "a" "a" "g" "c" "g" "t" "c" "g" "c" "t" "c" "c"
## [14707] "g" "a" "t" "a" "a" "t" "a" "a" "g" "g" "g" "c" "c" "g" "a" "a" "a" "g"
## [14725] "t" "g" "a" "c" "c" "c" "t" "g" "t" "a" "c" "g" "g" "g" "c" "a" "a" "g"
## [14743] "t" "t" "t" "g" "g" "c" "g" "c" "t" "c" "a" "g" "a" "c" "a" "g" "a" "a"
## [14761] "t" "a" "g" "c" "a" "a" "c" "g" "a" "c" "g" "c" "a" "t" "g" "t" "g" "c"
## [14779] "g" "t" "g" "t" "a" "a" "a" "a" "g" "a" "t" "a" "t" "g" "a" "a" "c" "a"
## [14797] "t" "t" "g" "a" "a" "a" "t" "a" "c" "g" "a" "g" "t" "g" "a" "g" "a" "t"
## [14815] "a" "g" "g" "g" "g" "a" "c" "g" "g" "a" "t" "a" "t" "c" "c" "a" "a" "c"
## [14833] "c" "c" "t" "t" "g" "a" "g" "a" "t" "c" "g" "g" "t" "a" "g" "t" "g" "t"
## [14851] "c" "c" "a" "g" "g" "g" "g" "a" "t" "a" "t" "g" "c" "t" "c" "a" "a" "t"
## [14869] "t" "a" "t" "c" "g" "c" "c" "c" "g" "t" "t" "a" "c" "g" "t" "c" "g" "t"
## [14887] "a" "a" "g" "c" "c" "t" "g" "t" "g" "a" "c" "a" "t" "g" "c" "g" "g" "g"
## [14905] "c" "t" "t" "c" "g" "a" "t" "c" "a" "c" "t" "c" "g" "c" "a" "g" "g" "a"
## [14923] "c" "t" "c" "c" "c" "a" "g" "c" "a" "t" "a" "g" "a" "c" "t" "g" "g" "a"
## [14941] "c" "c" "a" "g" "g" "g" "t" "t" "a" "a" "g" "g" "a" "t" "a" "a" "c" "g"
## [14959] "a" "c" "c" "g" "t" "t" "c" "c" "t" "a" "t" "g" "t" "c" "t" "t" "c" "g"
## [14977] "g" "t" "g" "g" "t" "c" "t" "g" "a" "t" "g" "g" "t" "t" "g" "t" "c" "g"
## [14995] "t" "c" "c" "a" "g" "t" "g" "c" "g" "t" "a" "c" "a" "g" "g" "t" "a" "t"
## [15013] "c" "g" "g" "c" "c" "g" "c" "g" "c" "t" "a" "a" "g" "c" "a" "t" "g" "a"
## [15031] "t" "c" "a" "t" "g" "t" "c" "g" "c" "g" "a" "a" "c" "t" "a" "t" "g" "a"
## [15049] "t" "t" "c" "c" "c" "c" "g" "g" "c" "a" "g" "t" "g" "t" "t" "g" "g" "g"
## [15067] "c" "g" "t" "a" "g" "g" "g" "t" "g" "c" "t" "t" "c" "c" "c" "c" "t" "g"
## [15085] "g" "t" "c" "a" "t" "g" "g" "g" "g" "t" "a" "t" "a" "a" "t" "a" "t" "g"
## [15103] "g" "a" "t" "c" "a" "g" "t" "g" "g" "a" "g" "c" "g" "c" "c" "g" "t" "g"
## [15121] "t" "a" "c" "t" "t" "c" "a" "a" "a" "c" "a" "a" "c" "a" "a" "a" "t" "a"
## [15139] "g" "a" "a" "t" "a" "a" "a" "t" "a" "c" "a" "t" "a" "t" "g" "t" "g" "g"
## [15157] "g" "a" "g" "g" "c" "a" "g" "g" "g" "c" "g" "a" "c" "t" "a" "g" "c" "g"
## [15175] "c" "t" "t" "c" "t" "c" "g" "c" "a" "g" "c" "t" "a" "a" "a" "c" "g" "a"
## [15193] "t" "g" "c" "g" "c" "c" "g" "g" "t" "a" "g" "t" "t" "g" "c" "c" "t" "a"
## [15211] "a" "a" "a" "a" "a" "g" "g" "c" "g" "g" "g" "a" "a" "a" "g" "t" "a" "t"
## [15229] "c" "a" "a" "a" "g" "t" "t" "c" "c" "t" "t" "c" "g" "c" "g" "g" "a" "c"
## [15247] "c" "g" "c" "c" "t" "c" "t" "c" "t" "c" "g" "a" "t" "a" "a" "t" "t" "a"
## [15265] "a" "a" "c" "g" "a" "a" "t" "g" "c" "a" "g" "c" "g" "a" "a" "t" "a" "a"
## [15283] "c" "c" "c" "a" "g" "a" "c" "t" "g" "a" "g" "a" "g" "c" "c" "t" "c" "c"
## [15301] "g" "g" "a" "g" "t" "g" "a" "c" "t" "g" "g" "a" "g" "g" "a" "c" "a" "c"
## [15319] "a" "c" "t" "g" "a" "c" "g" "a" "c" "g" "c" "a" "a" "g" "t" "c" "a" "c"
## [15337] "c" "g" "a" "a" "c" "a" "a" "g" "g" "t" "t" "g" "t" "a" "t" "c" "t" "c"
## [15355] "g" "a" "c" "a" "t" "t" "a" "g" "g" "g" "a" "a" "c" "g" "t" "c" "t" "a"
## [15373] "c" "a" "t" "g" "a" "g" "g" "g" "c" "a" "g" "c" "c" "g" "t" "a" "t" "g"
## [15391] "t" "t" "a" "g" "g" "a" "a" "g" "g" "g" "a" "a" "a" "t" "t" "g" "a" "g"
## [15409] "a" "a" "a" "g" "c" "a" "t" "g" "g" "t" "c" "t" "c" "a" "a" "a" "t" "g"
## [15427] "c" "t" "g" "t" "t" "a" "c" "a" "g" "a" "g" "c" "c" "a" "a" "c" "g" "c"
## [15445] "g" "g" "a" "g" "t" "t" "c" "a" "a" "a" "a" "c" "c" "g" "c" "a" "c" "a"
## [15463] "c" "g" "a" "t" "t" "g" "a" "a" "c" "a" "c" "c" "g" "a" "c" "a" "a" "a"
## [15481] "t" "a" "a" "a" "a" "g" "a" "c" "g" "g" "a" "t" "c" "t" "g" "c" "a" "g"
## [15499] "t" "c" "a" "t" "g" "g" "c" "g" "a" "g" "t" "g" "g" "g" "g" "a" "c" "a"
## [15517] "a" "a" "g" "c" "a" "a" "g" "c" "g" "c" "a" "a" "a" "a" "a" "g" "t" "a"
## [15535] "c" "a" "g" "c" "t" "t" "g" "a" "g" "t" "t" "t" "a" "t" "t" "a" "a" "g"
## [15553] "g" "g" "g" "c" "c" "a" "g" "g" "a" "t" "a" "g" "a" "a" "a" "c" "g" "g"
## [15571] "c" "c" "c" "g" "g" "c" "c" "a" "c" "g" "g" "a" "t" "t" "c" "t" "a" "g"
## [15589] "c" "g" "t" "a" "g" "t" "g" "a" "a" "a" "c" "t" "g" "a" "g" "c" "c" "g"
## [15607] "c" "c" "c" "c" "a" "c" "a" "g" "g" "c" "t" "a" "t" "a" "g" "c" "t" "t"
## [15625] "g" "c" "g" "g" "g" "c" "g" "c" "g" "c" "c" "g" "c" "t" "a" "t" "t" "a"
## [15643] "a" "g" "g" "g" "a" "c" "t" "c" "c" "c" "g" "t" "a" "t" "c" "a" "g" "a"
## [15661] "t" "g" "a" "a" "c" "c" "a" "t" "c" "g" "a" "a" "g" "g" "c" "a" "a" "g"
## [15679] "a" "g" "c" "g" "a" "t" "t" "t" "a" "c" "g" "a" "a" "t" "c" "g" "c" "c"
## [15697] "g" "c" "a" "g" "g" "g" "a" "g" "g" "c" "g" "c" "c" "t" "g" "c" "c" "g"
## [15715] "c" "c" "a" "g" "a" "c" "c" "c" "g" "t" "t" "c" "a" "c" "c" "c" "t" "c"
## [15733] "g" "a" "c" "a" "g" "c" "c" "g" "g" "c" "a" "g" "g" "a" "c" "t" "g" "g"
## [15751] "t" "c" "g" "g" "t" "t" "g" "t" "c" "c" "g" "t" "a" "t" "t" "c" "g" "t"
## [15769] "t" "g" "a" "g" "g" "g" "a" "a" "g" "a" "a" "g" "c" "a" "a" "t" "a" "a"
## [15787] "a" "t" "g" "g" "g" "a" "a" "a" "g" "g" "a" "g" "c" "a" "g" "c" "g" "t"
## [15805] "c" "g" "t" "g" "t" "g" "a" "a" "c" "a" "c" "a" "g" "t" "a" "g" "a" "g"
## [15823] "a" "a" "a" "a" "a" "g" "a" "g" "t" "t" "c" "t" "c" "a" "c" "g" "t" "g"
## [15841] "t" "c" "g" "g" "a" "a" "a" "t" "g" "c" "c" "a" "g" "a" "c" "c" "a" "c"
## [15859] "t" "t" "g" "a" "g" "g" "g" "g" "a" "g" "a" "a" "a" "c" "a" "c" "a" "c"
## [15877] "g" "g" "a" "g" "a" "a" "c" "c" "t" "t" "a" "t" "c" "a" "c" "g" "c" "g"
## [15895] "c" "a" "g" "t" "g" "a" "c" "a" "a" "t" "t" "c" "a" "g" "t" "g" "a" "a"
## [15913] "c" "a" "c" "t" "g" "c" "g" "g" "c" "c" "g" "c" "a" "g" "t" "c" "g" "c"
## [15931] "t" "c" "a" "a" "g" "t" "g" "t" "c" "a" "g" "a" "g" "g" "a" "c" "g" "g"
## [15949] "c" "c" "a" "a" "c" "a" "a" "t" "a" "a" "g" "t" "g" "g" "g" "g" "c" "a"
## [15967] "c" "a" "t" "c" "g" "c" "t" "g" "a" "a" "a" "a" "a" "c" "a" "g" "g" "g"
## [15985] "c" "g" "g" "g" "g" "g" "t" "c" "g" "a" "c" "g" "g" "g" "a" "a" "g" "t"
## [16003] "t" "g" "c" "a" "c" "g" "a" "g" "c" "c" "a" "g" "a" "t" "t" "g" "a" "c"
## [16021] "a" "c" "c" "g" "g" "g" "a" "a" "t" "t" "c" "g" "g" "a" "g" "g" "g" "g"
## [16039] "a" "t" "g" "t" "g" "a" "a" "t" "g" "t" "c" "t" "t" "g" "a" "g" "a" "c"
## [16057] "t" "g" "t" "g" "t" "g" "t" "t" "c" "g" "c" "c" "t" "t" "a" "a" "t" "t"
## [16075] "g" "c" "t" "g" "g" "c" "g" "a" "c" "a" "a" "c" "t" "t" "t" "g" "g" "g"
## [16093] "t" "g" "c" "t" "t" "c" "c" "a" "a" "g" "c" "a" "t" "a" "g" "g" "g" "t"
## [16111] "a" "a" "t" "t" "t" "t" "a" "a" "g" "g" "g" "a" "a" "c" "g" "a" "a" "t"
## [16129] "a" "c" "a" "c" "a" "t" "g" "t" "t" "a" "g" "g" "a" "c" "a" "t" "c" "c"
## [16147] "c" "a" "t" "g" "g" "g" "t" "g" "a" "g" "c" "c" "g" "g" "g" "c" "a" "g"
## [16165] "g" "a" "g" "a" "t" "c" "c" "a" "a" "a" "t" "g" "g" "c" "t" "g" "c" "c"
## [16183] "t" "a" "c" "g" "g" "a" "c" "t" "c" "a" "a" "g" "g" "t" "a" "c" "c" "c"
## [16201] "g" "g" "g" "c" "a" "c" "t" "c" "a" "c" "t" "c" "a" "a" "t" "a" "t" "g"
## [16219] "a" "c" "g" "c" "g" "c" "t" "a" "c" "c" "a" "g" "c" "c" "c" "g" "a" "g"
## [16237] "g" "g" "t" "t" "g" "g" "a" "t" "a" "t" "g" "c" "g" "c" "t" "c" "t" "a"
## [16255] "c" "a" "t" "t" "g" "g" "g" "t" "c" "g" "t" "a" "a" "g" "t" "t" "g" "t"
## [16273] "g" "t" "t" "t" "c" "c" "a" "t" "g" "g" "g" "t" "c" "a" "t" "t" "c" "c"
## [16291] "g" "a" "a" "a" "g" "g" "a" "c" "c" "c" "c" "a" "g" "c" "c" "c" "c" "a"
## [16309] "a" "t" "g" "g" "c" "a" "a" "t" "g" "t" "g" "g" "a" "g" "a" "c" "a" "t"
## [16327] "c" "t" "t" "a" "c" "g" "g" "g" "c" "c" "t" "g" "a" "g" "a" "c" "g" "g"
## [16345] "t" "t" "t" "a" "a" "t" "t" "t" "t" "t" "a" "c" "a" "t" "g" "c" "g" "g"
## [16363] "a" "g" "a" "t" "c" "g" "a" "g" "g" "a" "a" "t" "a" "c" "g" "t" "a" "g"
## [16381] "t" "t" "c" "t" "c" "a" "t" "t" "c" "g" "c" "g" "c" "g" "t" "c" "a" "a"
## [16399] "t" "t" "g" "a" "t" "a" "g" "g" "t" "t" "g" "t" "g" "a" "t" "a" "a" "t"
## [16417] "g" "g" "c" "g" "a" "g" "a" "t" "a" "t" "g" "g" "c" "g" "g" "a" "t" "c"
## [16435] "g" "a" "t" "t" "a" "g" "g" "c" "g" "t" "a" "t" "t" "t" "a" "g" "g" "a"
## [16453] "c" "g" "a" "c" "c" "g" "a" "g" "g" "g" "c" "g" "c" "c" "g" "a" "c" "c"
## [16471] "g" "g" "g" "g" "t" "g" "c" "c" "a" "a" "t" "t" "g" "t" "g" "g" "c" "a"
## [16489] "t" "a" "g" "t" "g" "a" "t" "c" "g" "a" "t" "g" "a" "c" "g" "t" "g" "c"
## [16507] "a" "g" "t" "t" "c" "a" "g" "a" "g" "c" "c" "a" "a" "c" "g" "a" "g" "g"
## [16525] "g" "g" "t" "c" "t" "g" "c" "c" "t" "c" "a" "c" "c" "g" "c" "t" "a" "g"
## [16543] "g" "c" "a" "a" "g" "c" "t" "g" "c" "a" "t" "a" "c" "g" "t" "a" "g" "g"
## [16561] "c" "a" "t" "t" "t" "t" "t" "a" "g" "a" "t" "g" "c" "c" "g" "t" "t" "a"
## [16579] "a" "t" "c" "g" "c" "a" "g" "c" "a" "a" "g" "a" "g" "a" "g" "t" "a" "g"
## [16597] "t" "a" "g" "a" "g" "a" "g" "t" "c" "g" "a" "g" "a" "c" "a" "a" "a" "c"
## [16615] "g" "g" "a" "g" "t" "g" "g" "c" "g" "c" "c" "a" "a" "t" "c" "c" "t" "c"
## [16633] "a" "a" "a" "c" "a" "c" "g" "g" "g" "c" "a" "g" "g" "g" "g" "g" "t" "a"
## [16651] "a" "a" "a" "g" "c" "g" "a" "g" "c" "a" "a" "c" "g" "g" "g" "g" "c" "c"
## [16669] "t" "a" "a" "t" "a" "a" "t" "a" "a" "a" "a" "g" "g" "g" "c" "g" "a" "g"
## [16687] "g" "t" "c" "a" "t" "c" "t" "t" "c" "a" "g" "t" "g" "g" "g" "c" "c" "t"
## [16705] "c" "c" "a" "g" "t" "t" "a" "g" "a" "a" "c" "a" "g" "a" "t" "t" "a" "t"
## [16723] "t" "g" "c" "g" "a" "t" "t" "c" "c" "a" "t" "g" "g" "t" "t" "a" "t" "g"
## [16741] "g" "c" "t" "a" "g" "c" "c" "c" "g" "a" "a" "a" "g" "c" "g" "t" "t" "t"
## [16759] "t" "g" "t" "t" "g" "t" "g" "a" "g" "a" "c" "c" "a" "g" "a" "a" "a" "t"
## [16777] "g" "a" "g" "a" "a" "g" "c" "a" "a" "a" "a" "t" "c" "t" "g" "g" "g" "a"
## [16795] "a" "a" "g" "g" "c" "a" "c" "c" "a" "c" "c" "a" "a" "g" "g" "g" "g" "a"
## [16813] "t" "a" "t" "g" "t" "t" "c" "t" "a" "g" "a" "c" "g" "g" "t" "a" "g" "a"
## [16831] "c" "a" "g" "t" "g" "g" "a" "t" "t" "g" "c" "a" "a" "g" "c" "a" "t" "a"
## [16849] "g" "c" "a" "t" "t" "g" "g" "c" "t" "g" "a" "g" "c" "t" "c" "g" "a" "t"
## [16867] "c" "a" "t" "t" "c" "g" "g" "t" "a" "g" "c" "g" "t" "c" "g" "t" "a" "a"
## [16885] "a" "g" "c" "t" "t" "a" "a" "g" "c" "t" "c" "a" "t" "g" "t" "c" "t" "g"
## [16903] "t" "c" "a" "t" "t" "c" "a" "g" "g" "g" "a" "g" "g" "g" "g" "c" "a" "g"
## [16921] "a" "c" "t" "g" "c" "g" "a" "c" "a" "g" "a" "c" "a" "a" "a" "c" "t" "g"
## [16939] "t" "g" "g" "c" "g" "c" "c" "t" "g" "t" "g" "a" "g" "g" "g" "a" "c" "t"
## [16957] "c" "a" "t" "c" "c" "a" "g" "g" "t" "g" "g" "g" "c" "c" "c" "a" "c" "g"
## [16975] "g" "t" "g" "a" "c" "t" "c" "g" "t" "g" "c" "g" "g" "a" "a" "c" "t" "t"
## [16993] "g" "a" "g" "g" "t" "g" "t" "g" "t" "a" "g" "c" "a" "g" "g" "t" "g" "g"
## [17011] "c" "t" "c" "a" "t" "a" "t" "g" "g" "t" "g" "g" "c" "a" "a" "g" "c" "g"
## [17029] "g" "g" "g" "c" "g" "g" "g" "g" "a" "c" "t" "t" "a" "c" "c" "t" "g" "c"
## [17047] "a" "a" "c" "c" "t" "g" "c" "c" "a" "t" "g" "g" "c" "t" "a" "a" "a" "t"
## [17065] "t" "a" "a" "t" "a" "a" "t" "c" "t" "g" "c" "a" "g" "a" "g" "a" "g" "t"
## [17083] "g" "a" "a" "a" "a" "g" "a" "t" "g" "t" "a" "g" "g" "g" "t" "a" "t" "g"
## [17101] "c" "t" "a" "g" "c" "t" "c" "g" "g" "a" "a" "t" "a" "g" "c" "t" "g" "c"
## [17119] "t" "c" "g" "a" "t" "t" "a" "t" "a" "g" "c" "c" "g" "t" "a" "c" "g" "t"
## [17137] "t" "c" "g" "a" "c" "g" "c" "a" "a" "a" "g" "c" "a" "a" "t" "g" "g" "t"
## [17155] "a" "c" "g" "g" "a" "c" "c" "c" "t" "c" "t" "t" "a" "c" "t" "c" "c" "g"
## [17173] "g" "a" "a" "g" "a" "a" "a" "c" "c" "g" "a" "t" "g" "t" "a" "c" "a" "t"
## [17191] "a" "g" "a" "t" "a" "c" "c" "a" "c" "g" "t" "c" "t" "t" "t" "c" "g" "t"
## [17209] "c" "a" "g" "a" "a" "g" "c" "g" "a" "t" "g" "g" "c" "c" "a" "a" "t" "g"
## [17227] "a" "g" "c" "c" "a" "g" "t" "t" "g" "a" "g" "g" "a" "g" "g" "a" "g" "g"
## [17245] "t" "g" "a" "a" "g" "c" "a" "c" "t" "a" "t" "g" "g" "g" "a" "t" "c" "g"
## [17263] "g" "c" "g" "a" "g" "g" "a" "t" "a" "g" "t" "g" "t" "g" "t" "c" "g" "t"
## [17281] "t" "t" "a" "t" "a" "g" "a" "c" "t" "a" "g" "c" "t" "g" "c" "g" "a" "t"
## [17299] "c" "g" "a" "a" "g" "c" "t" "c" "c" "a" "c" "c" "c" "c" "c" "g" "a" "a"
## [17317] "c" "c" "g" "a" "c" "a" "g" "g" "t" "a" "g" "g" "g" "a" "c" "a" "g" "a"
## [17335] "c" "c" "c" "c" "c" "g" "g" "a" "g" "g" "c" "a" "c" "g" "t" "t" "g" "c"
## [17353] "a" "a" "g" "t" "c" "a" "g" "a" "g" "t" "g" "t" "t" "g" "t" "t" "t" "c"
## [17371] "t" "g" "a" "t" "c" "t" "t" "a" "g" "t" "a" "t" "t" "a" "g" "c" "a" "g"
## [17389] "t" "a" "t" "g" "c" "c" "t" "a" "a" "a" "t" "g" "g" "c" "t" "a" "c" "g"
## [17407] "c" "a" "c" "a" "g" "g" "t" "c" "g" "a" "a" "c" "a" "t" "c" "a" "a" "g"
## [17425] "t" "c" "g" "t" "t" "c" "t" "a" "a" "c" "a" "a" "a" "g" "g" "a" "a" "g"
## [17443] "g" "a" "g" "g" "g" "t" "c" "t" "c" "c" "a" "t" "g" "c" "t" "g" "a" "c"
## [17461] "a" "g" "g" "g" "a" "g" "g" "c" "g" "c" "c" "c" "c" "g" "c" "t" "c" "a"
## [17479] "t" "t" "c" "t" "t" "a" "t" "a" "g" "a" "t" "t" "g" "g" "g" "g" "a" "a"
## [17497] "a" "c" "g" "a" "c" "a" "t" "t" "a" "g" "t" "c" "t" "t" "g" "c" "a" "a"
## [17515] "c" "t" "g" "t" "g" "c" "g" "a" "g" "a" "g" "g" "g" "a" "a" "c" "c" "c"
## [17533] "c" "c" "g" "c" "g" "c" "g" "g" "g" "c" "g" "c" "a" "a" "a" "g" "c" "c"
## [17551] "t" "c" "a" "a" "g" "g" "c" "t" "a" "t" "a" "g" "g" "c" "t" "c" "t" "a"
## [17569] "a" "c" "g" "c" "t" "g" "g" "c" "a" "g" "a" "t" "c" "g" "c" "t" "a" "t"
## [17587] "t" "a" "c" "g" "c" "a" "g" "c" "g" "c" "t" "c" "a" "a" "a" "c" "a" "a"
## [17605] "g" "t" "t" "t" "g" "t" "t" "t" "a" "a" "c" "c" "t" "t" "c" "g" "c" "g"
## [17623] "a" "t" "g" "a" "g" "t" "t" "a" "g" "g" "g" "c" "c" "g" "c" "g" "t" "c"
## [17641] "t" "g" "t" "t" "g" "g" "c" "a" "g" "a" "c" "g" "a" "c" "c" "t" "g" "a"
## [17659] "a" "g" "a" "g" "g" "g" "c" "g" "g" "t" "t" "t" "a" "t" "a" "c" "a" "g"
## [17677] "g" "g" "g" "c" "c" "t" "a" "a" "g" "t" "c" "c" "t" "g" "a" "t" "g" "t"
## [17695] "a" "g" "t" "c" "t" "t" "a" "c" "t" "c" "a" "g" "a" "t" "c" "t" "c" "t"
## [17713] "c" "a" "c" "g" "c" "c" "g" "c" "a" "t" "t" "a" "g" "c" "g" "a" "c" "g"
## [17731] "t" "g" "a" "t" "a" "g" "g" "t" "t" "g" "t" "g" "c" "g" "g" "g" "g" "a"
## [17749] "g" "a" "a" "a" "g" "g" "a" "a" "g" "c" "t" "c" "c" "g" "t" "t" "a" "c"
## [17767] "a" "a" "a" "t" "g" "t" "c" "g" "g" "g" "g" "g" "a" "a" "a" "c" "g" "c"
## [17785] "a" "c" "a" "g" "c" "a" "t" "a" "t" "a" "t" "t" "a" "a" "t" "g" "c" "g"
## [17803] "g" "a" "g" "a" "t" "t" "t" "g" "t" "c" "t" "a" "g" "a" "a" "c" "a" "g"
## [17821] "t" "c" "a" "g" "g" "a" "a" "a" "t" "g" "t" "g" "a" "t" "a" "t" "c" "t"
## [17839] "g" "a" "t" "g" "a" "a" "c" "t" "g" "g" "g" "c" "g" "t" "a" "a" "g" "g"
## [17857] "g" "g" "t" "g" "t" "t" "t" "c" "t" "g" "c" "g" "t" "c" "a" "a" "a" "g"
## [17875] "c" "g" "c" "t" "g" "c" "c" "t" "a" "g" "c" "g" "a" "t" "g" "a" "c" "g"
## [17893] "g" "c" "a" "c" "t" "g" "a" "c" "c" "t" "c" "a" "c" "c" "g" "c" "g" "t"
## [17911] "t" "t" "g" "a" "g" "a" "g" "g" "c" "g" "g" "a" "c" "g" "c" "t" "a" "a"
## [17929] "a" "t" "a" "a" "a" "c" "g" "g" "t" "g" "t" "c" "g" "c" "c" "a" "c" "g"
## [17947] "a" "g" "c" "g" "t" "t" "g" "c" "g" "t" "c" "a" "g" "t" "g" "a" "g" "t"
## [17965] "g" "a" "g" "g" "a" "c" "c" "g" "a" "g" "c" "g" "g" "a" "g" "a" "t" "a"
## [17983] "g" "g" "t" "c" "c" "g" "a" "t" "g" "a" "a" "g" "t" "g" "c" "t" "g" "c"
## [18001] "c" "t" "c" "a" "c" "a" "t" "g" "g" "t" "t" "a" "t" "c" "a" "a" "t" "g"
## [18019] "g" "g" "c" "g" "c" "c" "a" "t" "c" "g" "c" "a" "c" "g" "g" "c" "g" "c"
## [18037] "c" "c" "c" "g" "g" "a" "a" "t" "g" "a" "g" "g" "a" "g" "a" "a" "a" "a"
## [18055] "t" "t" "t" "g" "g" "t" "g" "a" "t" "g" "t" "t" "t" "a" "a" "g" "g" "c"
## [18073] "t" "t" "t" "c" "c" "c" "a" "g" "a" "g" "t" "c" "t" "g" "a" "a" "a" "c"
## [18091] "t" "t" "a" "t" "t" "g" "g" "c" "g" "g" "t" "t" "t" "g" "c" "a" "a" "g"
## [18109] "g" "g" "c" "a" "a" "t" "t" "t" "g" "t" "t" "a" "a" "a" "t" "g" "a" "g"
## [18127] "t" "a" "g" "g" "g" "t" "t" "c" "g" "g" "g" "g" "c" "t" "g" "g" "g" "a"
## [18145] "a" "g" "a" "t" "g" "a" "a" "a" "a" "a" "a" "t" "g" "c" "c" "c" "c" "g"
## [18163] "a" "c" "c" "t" "c" "t" "g" "a" "t" "a" "c" "a" "t" "g" "a" "g" "t" "g"
## [18181] "t" "a" "c" "g" "g" "a" "g" "a" "g" "a" "c" "g" "t" "g" "a" "a" "g" "c"
## [18199] "g" "t" "t" "g" "g" "g" "g" "t" "g" "t" "c" "g" "a" "c" "a" "a" "a" "g"
## [18217] "t" "c" "a" "a" "g" "t" "a" "g" "t" "t" "t" "a" "t" "t" "a" "t" "g" "g"
## [18235] "c" "c" "c" "c" "g" "t" "c" "a" "a" "g" "a" "g" "a" "t" "a" "g" "a" "c"
## [18253] "t" "a" "a" "t" "c" "g" "c" "g" "t" "c" "t" "a" "g" "c" "g" "g" "t" "a"
## [18271] "c" "c" "t" "t" "t" "a" "a" "c" "c" "a" "a" "a" "g" "t" "a" "t" "g" "g"
## [18289] "t" "a" "t" "g" "g" "t" "t" "a" "g" "c" "c" "g" "g" "t" "t" "a" "a" "g"
## [18307] "t" "a" "c" "a" "a" "g" "g" "g" "c" "t" "c" "g" "t" "c" "t" "g" "t" "t"
## [18325] "t" "a" "a" "a" "c" "a" "a" "c" "g" "g" "g" "t" "g" "g" "a" "a" "a" "g"
## [18343] "c" "t" "a" "c" "c" "g" "c" "g" "t" "a" "a" "g" "g" "c" "g" "t" "c" "g"
## [18361] "c" "t" "c" "a" "t" "t" "a" "g" "g" "a" "g" "a" "t" "g" "g" "t" "g" "g"
## [18379] "a" "c" "t" "t" "a" "c" "a" "c" "a" "a" "a" "a" "t" "t" "t" "g" "a" "g"
## [18397] "c" "c" "g" "c" "a" "a" "g" "a" "c" "a" "c" "g" "a" "a" "t" "t" "t" "g"
## [18415] "a" "a" "t" "t" "a" "c" "t" "t" "g" "g" "a" "g" "a" "g" "t" "c" "g" "g"
## [18433] "c" "c" "g" "c" "c" "c" "a" "t" "t" "t" "c" "t" "c" "a" "a" "a" "a" "g"
## [18451] "a" "t" "g" "t" "g" "g" "g" "c" "g" "c" "a" "t" "g" "t" "g" "a" "g" "a"
## [18469] "c" "g" "g" "a" "t" "t" "g" "a" "a" "g" "t" "a" "a" "a" "t" "g" "a" "g"
## [18487] "c" "g" "c" "g" "c" "t" "a" "c" "c" "t" "t" "c" "t" "a" "c" "a" "g" "a"
## [18505] "t" "t" "g" "t" "t" "t" "g" "t" "a" "g" "t" "t" "c" "t" "a" "g" "g" "a"
## [18523] "g" "t" "a" "c" "t" "c" "a" "c" "t" "c" "g" "c" "g" "g" "g" "a" "c" "t"
## [18541] "a" "t" "g" "a" "a" "g" "g" "g" "g" "g" "t" "t" "t" "c" "t" "a" "c" "t"
## [18559] "g" "g" "c" "a" "t" "a" "a" "a" "a" "t" "a" "g" "t" "c" "g" "c" "g" "g"
## [18577] "c" "g" "c" "a" "a" "a" "c" "g" "t" "g" "c" "g" "g" "t" "t" "g" "t" "a"
## [18595] "t" "a" "c" "a" "a" "c" "g" "g" "a" "g" "g" "g" "a" "t" "t" "a" "t" "t"
## [18613] "g" "g" "t" "c" "g" "g" "c" "a" "g" "g" "a" "a" "g" "g" "c" "t" "c" "t"
## [18631] "a" "c" "a" "a" "t" "a" "g" "a" "t" "g" "a" "c" "g" "t" "t" "g" "t" "c"
## [18649] "g" "g" "g" "t" "c" "t" "g" "g" "c" "a" "a" "a" "t" "a" "a" "t" "a" "a"
## [18667] "t" "t" "c" "c" "c" "a" "a" "g" "a" "c" "t" "a" "a" "g" "a" "c" "a" "t"
## [18685] "c" "c" "t" "a" "c" "c" "c" "a" "t" "t" "g" "a" "c" "c" "c" "a" "g" "c"
## [18703] "t" "c" "c" "g" "c" "a" "c" "a" "t" "a" "t" "c" "g" "g" "g" "t" "t" "c"
## [18721] "t" "g" "t" "c" "c" "c" "g" "c" "g" "t" "a" "g" "g" "c" "t" "a" "c" "g"
## [18739] "a" "t" "g" "c" "t" "c" "a" "g" "c" "a" "t" "g" "t" "c" "g" "c" "g" "c"
## [18757] "a" "c" "c" "a" "g" "a" "t" "a" "t" "a" "c" "a" "a" "a" "g" "c" "c" "c"
## [18775] "g" "g" "a" "t" "g" "a" "t" "t" "a" "a" "t" "g" "g" "g" "c" "a" "g" "t"
## [18793] "a" "a" "c" "t" "a" "t" "c" "g" "t" "t" "g" "t" "g" "a" "c" "g" "c" "g"
## [18811] "g" "g" "a" "a" "c" "a" "c" "a" "c" "c" "g" "c" "t" "c" "g" "g" "c" "g"
## [18829] "a" "g" "a" "t" "g" "t" "a" "c" "c" "g" "t" "g" "g" "a" "g" "a" "a" "a"
## [18847] "a" "a" "g" "t" "g" "g" "g" "a" "c" "t" "g" "g" "g" "a" "t" "g" "g" "c"
## [18865] "a" "a" "t" "t" "t" "g" "t" "g" "g" "t" "g" "t" "t" "g" "g" "t" "t" "g"
## [18883] "c" "g" "t" "a" "c" "c" "c" "t" "a" "a" "g" "t" "t" "g" "g" "a" "g" "a"
## [18901] "c" "t" "c" "c" "c" "t" "t" "c" "g" "g" "t" "a" "g" "c" "g" "c" "c" "c"
## [18919] "g" "t" "a" "a" "g" "g" "a" "c" "c" "c" "t" "t" "a" "g" "g" "g" "g" "c"
## [18937] "c" "t" "c" "g" "a" "g" "c" "a" "g" "a" "a" "c" "a" "t" "t" "a" "t" "c"
## [18955] "a" "g" "t" "a" "t" "a" "c" "a" "a" "a" "c" "a" "c" "a" "g" "a" "a" "a"
## [18973] "c" "c" "g" "a" "c" "a" "c" "c" "a" "c" "g" "g" "a" "g" "g" "c" "t" "a"
## [18991] "t" "a" "c" "g" "c" "t" "c" "c" "a" "a" "t" "c" "t" "g" "a" "c" "t" "c"
## [19009] "g" "g" "c" "c" "c" "c" "g" "g" "g" "a" "a" "t" "t" "c" "g" "g" "t" "c"
## [19027] "a" "c" "c" "a" "g" "g" "t" "a" "g" "a" "c" "c" "g" "g" "a" "t" "g" "c"
## [19045] "a" "a" "t" "c" "g" "g" "t" "g" "a" "t" "t" "a" "g" "t" "g" "g" "g" "a"
## [19063] "c" "a" "c" "t" "g" "c" "g" "g" "g" "g" "c" "a" "g" "t" "c" "g" "t" "c"
## [19081] "g" "g" "c" "t" "a" "c" "c" "g" "t" "g" "g" "a" "g" "a" "c" "g" "g" "g"
## [19099] "c" "g" "g" "a" "g" "t" "a" "a" "a" "a" "t" "t" "t" "t" "a" "t" "t" "c"
## [19117] "c" "a" "t" "a" "t" "g" "t" "g" "g" "c" "c" "c" "a" "t" "t" "c" "g" "g"
## [19135] "t" "c" "c" "g" "a" "g" "t" "a" "c" "t" "t" "t" "a" "c" "c" "g" "a" "t"
## [19153] "t" "t" "t" "a" "a" "g" "t" "a" "a" "g" "c" "c" "a" "g" "g" "t" "c" "c"
## [19171] "c" "g" "t" "g" "t" "g" "a" "a" "c" "g" "g" "a" "c" "t" "t" "a" "g" "g"
## [19189] "a" "t" "g" "t" "g" "g" "t" "a" "g" "g" "g" "a" "g" "c" "t" "a" "a" "a"
## [19207] "c" "t" "c" "g" "c" "a" "g" "c" "t" "g" "g" "c" "g" "t" "a" "a" "g" "a"
## [19225] "c" "a" "c" "a" "t" "c" "g" "c" "c" "c" "t" "t" "g" "c" "c" "a" "g" "a"
## [19243] "g" "a" "g" "c" "a" "a" "t" "t" "t" "g" "c" "c" "a" "g" "g" "a" "g" "a"
## [19261] "a" "a" "a" "a" "c" "c" "a" "c" "c" "t" "c" "g" "g" "a" "t" "g" "c" "a"
## [19279] "g" "a" "g" "a" "t" "t" "g" "g" "c" "a" "g" "c" "a" "a" "t" "a" "g" "c"
## [19297] "c" "c" "c" "c" "c" "g" "g" "g" "g" "t" "c" "t" "t" "t" "t" "c" "t" "c"
## [19315] "a" "a" "g" "g" "a" "g" "g" "a" "c" "g" "a" "a" "t" "a" "t" "a" "g" "a"
## [19333] "g" "a" "g" "t" "g" "a" "a" "a" "c" "a" "t" "a" "a" "g" "g" "c" "a" "g"
## [19351] "t" "g" "a" "a" "g" "g" "a" "a" "g" "a" "t" "c" "g" "a" "c" "g" "a" "a"
## [19369] "g" "c" "c" "c" "g" "t" "c" "c" "t" "a" "g" "c" "a" "c" "c" "a" "g" "c"
## [19387] "a" "a" "g" "t" "g" "g" "a" "t" "t" "c" "g" "g" "c" "c" "a" "g" "g" "t"
## [19405] "c" "a" "a" "g" "c" "t" "g" "g" "g" "c" "t" "a" "g" "g" "a" "g" "g" "g"
## [19423] "c" "g" "g" "t" "c" "t" "g" "t" "g" "c" "c" "t" "c" "a" "a" "t" "a" "a"
## [19441] "t" "g" "g" "c" "g" "a" "t" "a" "c" "g" "g" "t" "a" "a" "g" "g" "a" "t"
## [19459] "c" "c" "g" "a" "c" "g" "t" "t" "c" "c" "g" "g" "g" "g" "c" "a" "g" "g"
## [19477] "a" "t" "c" "c" "a" "g" "c" "t" "g" "a" "a" "t" "a" "g" "t" "c" "g" "c"
## [19495] "g" "g" "t" "a" "t" "t" "g" "g" "c" "c" "t" "g" "c" "t" "a" "a" "a" "c"
## [19513] "t" "g" "a" "t" "g" "g" "g" "t" "t" "t" "c" "c" "a" "a" "g" "g" "g" "c"
## [19531] "g" "g" "g" "g" "a" "g" "t" "c" "t" "t" "c" "g" "a" "a" "c" "g" "t" "c"
## [19549] "a" "t" "t" "a" "a" "g" "c" "g" "g" "t" "g" "c" "t" "a" "a" "t" "c" "g"
## [19567] "g" "t" "c" "a" "a" "c" "g" "g" "g" "a" "c" "g" "c" "g" "a" "a" "c" "t"
## [19585] "a" "g" "a" "g" "a" "g" "t" "t" "a" "c" "c" "c" "a" "c" "c" "c" "c" "a"
## [19603] "c" "c" "a" "a" "a" "a" "a" "a" "t" "g" "g" "t" "g" "c" "g" "a" "t" "a"
## [19621] "a" "c" "c" "g" "c" "a" "a" "g" "a" "g" "g" "a" "t" "a" "t" "g" "t" "t"
## [19639] "a" "g" "g" "t" "a" "g" "t" "t" "g" "a" "a" "g" "t" "t" "t" "a" "a" "a"
## [19657] "a" "a" "g" "a" "g" "g" "c" "g" "t" "c" "a" "t" "g" "a" "t" "c" "t" "t"
## [19675] "t" "g" "a" "g" "a" "g" "t" "c" "t" "c" "g" "c" "g" "c" "a" "t" "c" "g"
## [19693] "t" "a" "c" "c" "t" "t" "a" "g" "t" "a" "g" "c" "t" "t" "g" "g" "a" "a"
## [19711] "g" "c" "t" "a" "g" "g" "a" "g" "c" "g" "g" "g" "a" "c" "a" "a" "t" "a"
## [19729] "a" "a" "c" "a" "a" "g" "g" "g" "t" "a" "g" "g" "c" "t" "g" "c" "g" "g"
## [19747] "c" "g" "c" "c" "g" "a" "t" "t" "t" "c" "a" "g" "g" "a" "c" "c" "c" "g"
## [19765] "g" "a" "a" "g" "c" "c" "t" "t" "c" "g" "g" "c" "a" "a" "t" "c" "g" "t"
## [19783] "g" "c" "a" "t" "a" "a" "c" "c" "a" "c" "t" "g" "c" "c" "t" "a" "c" "g"
## [19801] "c" "t" "t" "a" "a" "t" "g" "g" "a" "c" "t" "c" "a" "t" "g" "g" "a" "t"
## [19819] "t" "t" "c" "c" "a" "t" "a" "t" "g" "t" "t" "g" "t" "a" "t" "g" "g" "c"
## [19837] "a" "a" "g" "c" "g" "c" "g" "g" "t" "c" "a" "t" "c" "t" "t" "t" "t" "a"
## [19855] "g" "g" "c" "t" "a" "g" "a" "c" "g" "c" "t" "g" "c" "a" "g" "c" "a" "c"
## [19873] "g" "g" "c" "c" "c" "g" "t" "a" "t" "a" "a" "g" "g" "g" "g" "g" "t" "t"
## [19891] "a" "g" "c" "g" "g" "g" "g" "a" "g" "c" "t" "c" "a" "a" "a" "t" "a" "g"
## [19909] "t" "g" "g" "c" "c" "c" "g" "t" "a" "g" "a" "t" "c" "t" "a" "a" "t" "g"
## [19927] "c" "g" "t" "t" "g" "a" "c" "t" "t" "a" "g" "c" "a" "g" "g" "a" "g" "c"
## [19945] "g" "a" "c" "c" "g" "c" "c" "g" "a" "g" "g" "t" "t" "a" "c" "g" "a" "a"
## [19963] "a" "c" "g" "c" "a" "a" "c" "a" "c" "a" "c" "a" "a" "a" "c" "t" "g" "g"
## [19981] "g" "t" "a" "c" "g" "t" "c" "a" "g" "g" "a" "t" "c" "t" "c" "c" "c" "g"
## [19999] "a" "g"

Reliability of drifting Markov models

The reliability measures are computed by means of the following functions: A (availability), R (reliability,survival function), M (maintainability), errorRate (the classical failure rate, called BMP-failure rate and a more recent failure rate adapted to discrete data, called RG-failure rate). For more details on these reliability measures one can see Barbu and Limnios (2004); Barbu and Limnios (2008). All these functions have the following arguments:

x: An object of class dmm
k1: An integer, start position for the computation of the corresponding reliability measure
k2: An integer, end position for the computation of the corresponding reliability measure
s1: Character vector of the subspace working states (up-states) among the state space vector s.t. s1 < s
output_file: File containing the estimated/computed values of the corresponding reliability measure at each position of the selected frame
plot: display figure plot of the corresponding reliability measure along the positions if TRUE

The function errorRate enables to select the type of evaluated failure rate with an additional argument :

error.rate: Default="BMP", then BMP-failure-rate is the method used to estimate the error rate. If error.rate= "RG", then RG-failure rate is the method used to estimate the error rate.

These functions return vectors with the values of the corresponding reliability measure.

Estimation of reliability

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c("a","c","g","t"), init.estim ="freq", fit.method="sum")
reliability(dmm, k1=1, k2=10, upstates=c("a","c"),output_file = "file.txt", plot=TRUE)
## [[1]]
##       positions  reliability
##  [1,]         1 0.4885571729
##  [2,]         2 0.2411445408
##  [3,]         3 0.1188995038
##  [4,]         4 0.0586239943
##  [5,]         5 0.0289048794
##  [6,]         6 0.0142517252
##  [7,]         7 0.0070269076
##  [8,]         8 0.0034646676
##  [9,]         9 0.0017082814
## [10,]        10 0.0008422825
## 
## [[2]]

Estimation of availability

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c("a", "c", "g", "t"), init.estim = "freq", fit.method="sum")
availability(dmm, k1=1, k2=10, upstates=c("a","c"), output_file = "file.txt", plot=TRUE)
## [[1]]
##       positions availability
##  [1,]         1    0.4690808
##  [2,]         2    0.4761674
##  [3,]         3    0.4766474
##  [4,]         4    0.4766457
##  [5,]         5    0.4766422
##  [6,]         6    0.4766424
##  [7,]         7    0.4766428
##  [8,]         8    0.4766432
##  [9,]         9    0.4766436
## [10,]        10    0.4766440
## 
## [[2]]

Estimation of maintainability

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c("a","c","g","t"), init.estim="freq", fit.method="sum")
maintainability(dmm, k1=1, k2=10, upstates=c("a","c"), output_file = "file.txt", plot=TRUE)
## [[1]]
##       positions maintainability
##  [1,]         1       0.4885572
##  [2,]         2       0.7164935
##  [3,]         3       0.8485148
##  [4,]         4       0.9189865
##  [5,]         5       0.9566753
##  [6,]         6       0.9768307
##  [7,]         7       0.9876094
##  [8,]         8       0.9933737
##  [9,]         9       0.9964564
## [10,]        10       0.9981049
## 
## [[2]]

Estimation of failure rates

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c("a","c","g","t"), init.estim="freq", fit.method="sum")
failureRate(dmm, k1=1, k2=10, upstates=c("a","c"), failure.rate="BMP", output_file="file.txt", plot=TRUE)
## [[1]]
##       positions       BMP
##  [1,]         1 0.5064149
##  [2,]         2 0.5069368
##  [3,]         3 0.5069450
##  [4,]         4 0.5069446
##  [5,]         5 0.5069440
##  [6,]         6 0.5069434
##  [7,]         7 0.5069428
##  [8,]         8 0.5069422
##  [9,]         9 0.5069416
## [10,]        10 0.5069410
## 
## [[2]]

Concluding remarks

To conclude, in this paper we have presented drimmR, an R package for simulation, estimation and reliability and survival analysis of drifting Markov models. These are versatile stochastic models of Markov type capable of taking into account a time non-homogeneity of a known, controlled shape. For this reason these models can represent interesting modeling alternatives to classical models (like Markov models, semi-Markov models, etc.) and can be useful for researchers, practitioners and engineers in various fields.

The package addresses several items important from practical point of view, when carrying out the estimation: we consider one or several samples, the sample paths can be complete or not, can come from models of the same length or of different lengths.

The fields of application of the DMMs can be numerous; we only want to point out three of them.

Survival analysis and reliability theory: note that important indicators like reliability or survival function, availability, maintainability and failure rates are computed in our package;
Bioinformatics: note that important quantities for OMICS data in general, DNA analysis in particular, are computed by the proposed package. Thus we have the computation of the probabilities and expectations of appearance of a given word along the sequence.

Flowchart of the drimmR package.

Barbu, Vlad Stefan, Caroline Bérard, Dominique Cellier, Mathilde Sautreuil, and Nicolas Vergne. 2018. “SMM: An R Package for Estimation and Simulation of Discrete-Time Semi-Markov Models.” R Journal 10 (2).

Barbu, Vlad Stefan, Geoffray Brelurut, Annthomy Gilles, Arnaud Lefebvre, Victor Mataigne, and Nicolas Vergne. 2018. “DRIMM’R and Webdrimm: An R Package and a Web Interface for Drifting Markov Model Estimation and Reliability.” In JDS. Paris, France. https://hal-normandie-univ.archives-ouvertes.fr/hal-02337261.

Barbu, Vlad Stefan, and Nikolaos Limnios. 2004. “Discrete Time Semi-Markov Processes for Reliability and Survival Analysis - a Nonparametric Estimation Approach.” In Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis and Quality of Life, edited by M. Nikulin, N. Balakrishnan, M. Mesbah, and N. Limnios, 487–502. Statistics for Industry and Technology. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8206-4_30.

———. 2008. “Reliability of Semi-Markov Systems in Discrete Time: Modeling and Estimation.” In Handbook on Performability Engineering, edited by K. B. Misra, 369–80. Springer. https://doi.org/10.1007/978-1-84800-131-2_24.

Barbu, Vlad Stefan, and Nicolas Vergne. 2019. “Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation.” Methodology and Computing in Applied Probability 21 (4): 1407–29.

Bulla, Jan, Ingo Bulla, and Oleg Nenadić. 2010. “Hsmm — an R Package for Analyzing Hidden Semi-Markov Models.” Computational Statistics & Data Analysis, Second Special Issue on Statistical Algorithms and computer software, 54 (3): 611–19. https://doi.org/10.1016/j.csda.2008.08.025.

Król, Agnieszka, and Philippe Saint-Pierre. 2015. “SemiMarkov : An R Package for Parametric Estimation in Multi-State Semi-Markov Models.” Journal of Statistical Software 66 (6). https://doi.org/10.18637/jss.v066.i06.

O’Connell, Jared, and Søren Højsgaard. 2011. “Hidden Semi Markov Models for Multiple Observation Sequences: The Mhsmm Package for R.” Journal of Statistical Software 39 (4). https://doi.org/10.18637/jss.v039.i04.

Vergne, Nicolas. 2008. “Drifting Markov Models with Polynomial Drift and Applications to Dna Sequences.” Statistical Applications in Genetics and Molecular Biology 7 (1). https://doi.org/10.2202/1544-6115.1326.