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;
typedef long long ll;
const int N = 1000000 + 10;
char s[N];
int a[N];
int main(){
    int n; scanf("%d",&n);
    scanf("%s",s);
    if(n==1) return 0 * printf("%s",s);
    int cnt = 0;
    for(int i=0;i<n;i++) a[i] = s[i] - '0' - 1, cnt |= (a[i]==1);
    if(cnt){
        int ans = 0;
        for(int i=0;i<n;i++) if((i&(n-1))==i) ans ^= (a[i]%2);
        printf("%d\n",ans);
    }
    else{
        int ans = 0;
        for(int i=0;i<n;i++) if((i&(n-1))==i) ans ^= (a[i]/2);
        printf("%d\n",ans*2);
    }
}