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>
#include <stdlib.h>

int converte(char a) {
    if (a=='1')
        return 1;
    else if(a=='2')
        return 2;
    return 3;
}

int main() {
    int n, zz;
    scanf("%d", &n);
    char num[n];
    int v[n];
    scanf("%s", num);
    for (int j=0; j<n; ++j) {
        v[j]=converte(num[j]);
        //printf("%d ", v[j]);
    }
    zz = n-1;
    while(zz) {
        for(int i=0; i<zz; ++i) {
            v[i] = abs(v[i]-v[i+1]);
            //printf("%d ", v[i]);
        }
        //printf("\n");
        --zz;
    }
    /*for (int i=1; i<n; ++i) {
        pro_l = n-i;
        for (int j=0; j<pro_l; ++j)
            v[i][j] = abs(v[i-1][j] - v[i-1][j+1]);
    }*/
    printf("%d\n", v[0]);
    return 0;
}