Consider the following experiment: we roll two dice consecutively. The first die

Question

Consider the following experiment: we roll two dice consecutively. The first die is fair. If the first roll is a 1, 2, or 3, we roll the same die again. If the first roll yields a 4, 5, or 6, then we roll an unfair die with probabilities [0 0 0 1/3 1/3 1/3].

What is the probability of the outcome (1,6) (the first roll is a 1 and the second is a 6)?

What is the probability of the outcome (6,1)?

What is the probability of the outcome (6, 6)?

Please write a matlab script to simulate this experiment. Run 1000 trials of this experiment.

MatLab File so far...

function index =rollDice(prob)
prob=geneCumulative(prob);
y_init=rand();%generate a Int from [1,6] with fair chance.
y_tmp=prob-y_init;
index=6;
for i =1:6
if(y_tmp(i)>=0)
index=i;
break;
end
end

end

Explanation / Answer

As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 4 , 4 )
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 6 , 4 )
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 5 , 3 )
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 4 , 5 )
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 4 , 4 )
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 5 , 4 )
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 6 , 3 )
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 6 , 4 )
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 5 , 5 )
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
The pair of dice values are: ( 5 , 5 )

As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice

As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 5 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 3 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 2 is in between 1 and 3, we will roll the first dice again
As the first dice value of 6 is in between 4 and 6, we will roll the 2nd dice
As the first dice value of 1 is in between 1 and 3, we will roll the first dice again
As the first dice value of 4 is in between 4 and 6, we will roll the 2nd dice

1000 random numbers between 1 to 6 to be used in dice rolling
1   2   2   2   1   3   1   1   4   5   6   5   2   4   2   1   1   6   2   5   4   2   1   3   6   5   2   4   5   3   1   5   1   2   1   1   5   3   5   5   3   3   5   4   2   5   4   2   6   1   1   5   5   6   2   1   2   3   4   5   6   3   3   2   4   2   2   2   2   4   4   3   1   2   3   2   3   5   6   5   6   6   4   3   6   4   2   6   6   4   2   5   2   2   1   2   2   5   2   4   5   3   6   1   3   4   1   6   5   2   1   1   1   3   1   3   5   3   2   4   1   6   5   2   3   4   3   4   5   2   5   2   1   4   6   1   5   1   5   2   2   2   2   5   2   2   2   3   4   5   6   5   1   1   1   1   1   6   6   4   4   5   3   4   2   5   2   1   1   5   6   1   4   4   5   4   2   2   1   1   3   3   4   5   4   6   6   5   3   3   1   6   4   3   3   5   2   3   1   3   6   3   4   3   5   6   4   3   6   3   4   5   4   4   3   3   1   2   2   6   6   6   3   5   3   3   2   5   1   1   1   6   6   1   3   4   6   6   2   2   5   2   3   6   3   6   2   1   1   4   2   6   2   3   2   5   3   5   4   2   4   6   5   4   1   6   2   1   3   6   5   4   6   5   6   2   5   4   4   3   4   2   2   1   1   1   2   2   1   3   3   2   3   1   4   5   4   2   1   5   3   2   5   3   4   4   4   2   2   1   5   1   2   4   5   6   6   3   2   6   3   5   3   4   2   4   1   5   6   3   3   6   1   2   1   3   2   4   1   5   3   2   4   1   4   6   5   2   6   1   3   5   5   1   1   2   5   3   3   2   5   2   5   3   1   4   1   4   1   5   2   2   1   1   3   4   4   6   1   5   6   4   2   1   4   4   3   6   1   1   1   1   5   1   5   5   3   6   2   3   3   3   5   2   2   4   3   2   6   1   3   5   2   1   2   6   5   5   4   5   4   2   6   4   1   6   4   1   2   4   4   4   1   4   5   5   6   2   4   3   1   4   5   3   4   6   4   1   6   2   4   4   1   2   1   5   5   5   1   2   1   6   2   4   6   1   6   6   2   5   5   1   6   6   5   5   3   6   5   6   5   2   2   5   2   3   5   2   4   6   2   1   6   6   2   2   1   2   1   2   1   3   6   6   5   3   1   4   4   2   5   1   5   6   6   4   4   6   3   2   4   4   1   4   4   1   1   3   1   5   1   2   5   2   1   3   2   5   5   3   3   4   4   3   4   1   2   6   2   6   6   5   5   2   2   6   6   1   6   6   3   1   6   5   1   3   3   6   2   6   5   6   5   5   1   3   5   1   2   5   2   6   2   4   2   2   5   4   4   6   2   3   4   2   4   3   4   1   3   1   1   5   1   6   2   6   4   5   2   6   2   1   1   4   2   4   6   2   6   3   6   1   2   5   1   2   1   5   4   1   6   6   5   5   3   3   1   4   6   6   3   2   6   3   3   5   2   3   5   2   1   6   5   3   1   2   3   2   3   6   1   3   1   5   3   5   2   5   5   5   5   6   5   4   2   5   5   4   4   1   3   4   5   3   4   6   6   4   4   4   4   1   2   6   2   6   4   3   1   2   2   2   2   3   2   3   2   4   3   1   3   3   3   1   4   1   5   3   2   5   5   2   4   1   4   3   5   3   4   5   6   4   2   6   5   4   3   2   2   4   3   1   3   1   1   4   5   1   5   1   6   4   4   5   5   1   1   6   5   3   5   5   4   6   4   1   5   5   1   5   2   4   1   5   6   3   4   2   6   2   1   1   4   1   1   5   5   1   2   6   1   4   6   4   5   2   5   6   3   2   6   3   4   3   4   1   3   1   2   5   4   5   3   4   1   2   3   4   3   6   1   2   4   4   5   6   6   1   1   4   2   5   2   5   2   3   6   6   1   3   3   3   5   1   5   2   1   5   3   2   4   1   6   6   4   6   1   1   1   6   5   3   5   4   1   1   1   5   1   1   1   5   6   2   2   6   6   3   3   6   5   2   2   1   3   1   4   4   1   4   3   4   1   4   1   3   6   1   3   4   1   6   4   4   2   1   1   5   3   2   3   6   1   4   4   1   1   6   4   4   1   1   2   2   2   4   5   6   4   1   1   5   3   2   5   4   5   5   3   3   2   2   4   3   4   4   2   5   1   6   5   4   1   2   6   6   5   1   4   2   1   1   4   5   6   2   1   3   1   1   4   2   4   6   4   1   4   3   5   6   6   1   5   2   3   5   3   1   4   2   5   5   1   4   6   5   1   1   5   4   1   2   2   2   1   3   1   1   4   5   6   5   2   4   2   1   1   6   2   5   4   2   1   3   6   5   2   4   5   3   1   5   1   2   1   1   5   3   5   5   3   3   5   4   2   5   4   2   6   1   1   5   5   6   2   1   2   3   4   5   6   3   3   2   4   2   2   2   2   4   4   3   1   2   3   2   3   5   6   5   6   6   4   3   6   4   2   6   6   4   2   5   2   2   1   2   2   5   2   4   5   3   6   1   3   4   1   6   5   2   1   1   1   3   1   3   5   3   2   4   1   6   5   2   3   4   3   4   5   2   5   2   1   4   6   1   5   1   5   2   2   2   2   5   2   2   2   3   4   5   6   5   1   1   1   1   1   6   6   4   4   5   3   4   2   5   2   1   1   5   6   1   4   4   5   4   2   2   1   1   3   3   4   5   4   6   6   5   3   3   1   6   4   3   3   5   2   3   1   3   6   3   4   3   5   6   4   3   6   3   4   5   4   4   3   3   1   2   2   6   6   6   3   5   3   3   2   5   1   1   1   6   6   1   3   4   6   6   2   2   5   2   3   6   3   6   2   1   1   4   2   6   2   3   2   5   3   5   4   2   4   6   5   4   1   6   2   1   3   6   5   4   6   5   6   2   5   4   4   3   4   2   2   1   1   1   2   2   1   3   3   2   3   1   4   5   4   2   1   5   3   2   5   3   4   4   4   2   2   1   5   1   2   4   5   6   6   3   2   6   3   5   3   4   2   4   1   5   6   3   3   6   1   2   1   3   2   4   1   5   3   2   4   1   4   6   5   2   6   1   3   5   5   1   1   2   5   3   3   2   5   2   5   3   1   4   1   4   1   5   2   2   1   1   3   4   4   6   1   5   6   4   2   1   4   4   3   6   1   1   1   1   5   1   5   5   3   6   2   3   3   3   5   2   2   4   3   2   6   1   3   5   2   1   2   6   5   5   4   5   4   2   6   4   1   6   4   1   2   4   4   4   1   4   5   5   6   2   4   3   1   4   5   3   4   6   4   1   6   2   4   4   1   2   1   5   5   5   1   2   1   6   2   4   6   1   6   6   2   5   5   1   6   6   5   5   3   6   5   6   5   2   2   5   2   3   5   2   4   6   2   1   6   6   2   2   1   2   1   2   1   3   6   6   5   3   1   4   4   2   5   1   5   6   6   4   4   6   3   2   4   4   1   4   4   1   1   3   1   5   1   2   5   2   1   3   2   5   5   3   3   4   4   3   4   1   2   6   2   6   6   5   5   2   2   6   6   1   6   6   3   1   6   5   1   3   3   6   2   6   5   6   5   5   1   3   5   1   2   5   2   6   2   4   2   2   5   4   4   6   2   3   4   2   4   3   4   1   3   1   1   5   1   6   2   6   4   5   2   6   2   1   1   4   2   4   6   2   6   3   6   1   2   5   1   2   1   5   4   1   6   6   5   5   3   3   1   4   6   6   3   2   6   3   3   5   2   3   5   2   1   6   5   3   1   2   3   2   3   6   1   3   1   5   3   5   2   5   5   5   5   6   5   4   2   5   5   4   4   1   3   4   5   3   4   6   6   4   4   4   4   1   2   6   2   6   4   3   1   2   2   2   2   3   2   3   2   4   3   1   3   3   3   1   4   1   5   3   2   5   5   2   4   1   4   3   5   3   4   5   6   4   2   6   5   4   3   2   2   4   3   1   3   1   1   4   5   1   5   1   6   4   4   5   5   1   1   6   5   3   5   5   4   6   4   1   5   5   1   5   2   4   1   5   6   3   4   2   6   2   1   1   4   1   1   5   5   1   2   6   1   4   6   4   5   2   5   6   3   2   6   3   4   3   4   1   3   1   2   5   4   5   3   4   1   2   3   4   3   6   1   2   4   4   5   6   6   1   1   4   2   5   2   5   2   3   6   6   1   3   3   3   5   1   5   2   1   5   3   2   4   1   6   6   4   6   1   1   1   6   5   3   5   4   1   1   1   5   1   1   1   5   6   2   2   6   6   3   3   6   5   2   2   1   3   1   4   4   1   4   3   4   1   4   1   3   6   1   3   4   1   6   4   4   2   1   1   5   3   2   3   6   1   4   4   1   1   6   4   4   1   1   2   2   2   4   5   6   4   1   1   5   3   2   5   4   5   5   3   3   2   2   4   3   4   4   2   5   1   6   5   4   1   2   6   6   5   1   4   2   1   1   4   5   6   2   1   3   1   1   4   2   4   6   4   1   4   3   5   6   6   1   5   2   3   5   3   1   4   2   5   5   1   4   6   5   1   1   5   4

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