#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int max_n=1000005;
char s[max_n];
int n,a[max_n];
int solve(){
    int res=0;
    for(int i=0;i<n;i++)if((i&(n-1))==i)res+=a[i];
    return res&1;
}
int main(){
    scanf("%d %s",&n,s);
    for(int i=0;i<n;i++)a[i]=s[i]-'1';
    if(solve())printf("1\n");
    else{
        bool f=false;
        for(int i=0;i<n;i++)f|=a[i]==1;
        if(f)printf("0\n");
        else{
            for(int i=0;i<n;i++)a[i]/=2;
            if(solve())printf("2\n");
            else printf("0\n");
        }
    }
    return 0;
}
### Prompt

Please formulate a CPP solution to the following 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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int max_n=1000005;
char s[max_n];
int n,a[max_n];
int solve(){
    int res=0;
    for(int i=0;i<n;i++)if((i&(n-1))==i)res+=a[i];
    return res&1;
}
int main(){
    scanf("%d %s",&n,s);
    for(int i=0;i<n;i++)a[i]=s[i]-'1';
    if(solve())printf("1\n");
    else{
        bool f=false;
        for(int i=0;i<n;i++)f|=a[i]==1;
        if(f)printf("0\n");
        else{
            for(int i=0;i<n;i++)a[i]/=2;
            if(solve())printf("2\n");
            else printf("0\n");
        }
    }
    return 0;
}
```