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;

const int Maxn = 1000005;

int n;
char a[Maxn];

int Has(int r, int c)
{
    while (r) {
        if (c % 2 > r % 2) return 0;
        c /= 2; r /= 2;
    }
    return 1;
}

int main()
{
    scanf("%d", &n);
    scanf("%s", a);
    for (int i = 0; i < n; i++)
        a[i]--;
    bool was1 = false;
    bool odd = false;
    for (int i = 0; i < n; i++)
        if (a[i] == '1') { odd ^= Has(n - 1, i); was1 = true; }
    if (odd) { printf("1\n"); return 0; }
    if (was1) { printf("0\n"); return 0; }
    for (int i = 0; i < n; i++)
        if (a[i] == '2') odd ^= Has(n - 1, i);
    printf("%d\n", odd? 2: 0);
    return 0;
}