#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
#define ll long long 
#define il inline
const int maxn=1000010;
il int read(){
    char ch=getchar();
    while (ch<'0'||ch>'9') ch=getchar();
    return ch-'0';
}
int n,a[maxn];
int odd1,occured1,odd2;
int main(){
    scanf("%d",&n); n--;
    for (int i=0;i<=n;++i){
        a[i]=read()-1; if (a[i]==1) occured1=1;
    }
    for (int i=0;i<=n;++i){
        if ((i&n)==i){
            if (a[i]==1) {odd1^=1;}
            else if (a[i]==2) odd2^=1;
        }
    }
    if (odd1){printf("1"); exit(0);}
    if (odd2&&!occured1){printf("2"); exit(0);}
    printf("0");
    return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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

### Response

```cpp
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
#define ll long long 
#define il inline
const int maxn=1000010;
il int read(){
    char ch=getchar();
    while (ch<'0'||ch>'9') ch=getchar();
    return ch-'0';
}
int n,a[maxn];
int odd1,occured1,odd2;
int main(){
    scanf("%d",&n); n--;
    for (int i=0;i<=n;++i){
        a[i]=read()-1; if (a[i]==1) occured1=1;
    }
    for (int i=0;i<=n;++i){
        if ((i&n)==i){
            if (a[i]==1) {odd1^=1;}
            else if (a[i]==2) odd2^=1;
        }
    }
    if (odd1){printf("1"); exit(0);}
    if (odd2&&!occured1){printf("2"); exit(0);}
    printf("0");
    return 0;
}
```