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;

int n, x[1000010], a[1000010];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%1d", &x[i]);
    }
    for (int i = 1; i < n; i++) {
        a[i] = abs(x[i] - x[i + 1]);
    }
    n--;
    bool flag = 1;
    for (int i = 1; i <= n; i++) {
        flag &= (a[i] == 0 || a[i] == 2);
    }
    int ans = 0;
    for (int i = 1; i <= n; i++) {
        if (flag && a[i] == 2) a[i] = 1;
        if (((n - 1) & (i - 1)) == (i - 1)) (ans += a[i]) %= 2;
    }
    if (flag && ans) ans = 2;
    printf("%d\n", ans);
    return 0;
}