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>
#define Rint register int
using namespace std;
const int N = 1000003;
int n, a[N], ans;
bool f;
int main(){
    scanf("%d", &n);
    for(Rint i = 0;i < n;++ i){
        scanf("%1d", a + i); -- a[i]; f |= a[i] == 1;
    }
    if(!f) for(Rint i = 0;i < n;++ i) a[i] >>= 1;
    for(Rint i = 0;i < n;++ i) if(!(i & n - 1 - i)) ans ^= a[i] & 1;
    if(!f) ans <<= 1;
    printf("%d", ans);
}