Problem:
Score : 700 points

Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3.
Let x_{i,j} defined as follows:

x_{1,j} := a_j \quad (1 \leq j \leq N)

x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

Constraints

2 \leq N \leq 10^6

a_i = 1,2,3 (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N

Output

Print x_{N,1}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
define("MOD", 100);
$n = intval(trim(fgets(STDIN)));
$s = trim(fgets(STDIN));
$n = strlen($s);
$kigu = 0;
for($i = 0; $i < $n; ++$i){
    $dp[$i] = ((int)$s[$i])-1;
    $kigu ^= ($dp[$i]%2) * ((($n-1) & $i) == $i);
}
if($kigu){
    echo 1;
}else{
    if(array_search(1, $dp)!==false){
        echo 0;
    }else{
        $kigu = 0;
        for($i = 0; $i < $n; ++$i){
            $kigu ^= (($dp[$i]/2)%2) * ((($n-1) & $i) == $i);
        }
        if($kigu){
            echo 2;
        }else{
            echo 0;
        }
    }
}