Problem: 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}.

Examples

Input

4
1231


Output

1


Input

10
2311312312


Output

0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

// nCr % 2
int comb(int n, int r){
    int t = 0;
    int a=n, b=r, c=n-r;
    while(a){ a/=2; t += a; }
    while(b){ b/=2; t -= b; }
    while(c){ c/=2; t -= c; }
    return t?0:1;
}

char str[1000010];

int main()
{
    int n, ans = 0;
    scanf("%d%s", &n, str);
    // only 3
    for(int i=0; i<n; ++i){
        if(str[i]!='3') continue;
        ans ^= comb(n-1, i);
    }
    ans *= 2;
    // only 2
    for(int i=0; i<n; ++i){
        if(str[i]!='2') continue;
        if(ans==2) ans = 0;
        ans ^= comb(n-1, i);
    }
    printf("%d\n", ans);
}