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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
int main()
{
    char line[10000000];
    int size;
    int i;
    int j;
    int temp;
    int index_i;
    int index_j;

    fgets(line, sizeof(line), stdin);
    sscanf(line, "%d", &size);
    fgets(line, sizeof(line), stdin);
    

    for(index_i = 0; index_i < size; ++index_i){
        for(index_j = 0; index_j < (size - index_i - 1); ++index_j){
            i = (int)(line[index_j] - '0');
            j = (int)(line[index_j + 1] - '0');
            temp = i - j;
            if(temp < 0)
                temp *= -1;
            
            line[index_j] = temp + '0';
          //printf("%c\n", line[index_j]);
        }
    }
    printf("%c\n", line[0]);
    return 0;
}