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;
char s[1000008];
int n,i,j,k,a[1000008];
int main() {
    for(scanf("%d%s",&n,s+1),--n; i++<n;
            i&1?0:a[i]=1+a[i>>1],j|=1==(s[i-1]=abs(s[i]-s[i+1])));
    if(j)
        for(i=n; i--; s[i]&=1);
    for(--n,k=s[i=j=0]; i++<n; (j+=a[n+1-i]-a[i])?0:k^=s[i]);
    printf("%d\n",k),exit(0);
}