#include<bits/stdc++.h>
using namespace std;
const int maxn=1e6+3;
int n,a[maxn],b[maxn];
char s[maxn];
int solve(){
    int ret=0;
    for (int i=0;i<=n-1;i++) if ((i&(n-1))==i) ret^=b[i];
    return ret;
}
int main(){
    cin >> n >> s;
    for (int i=0;i<n;i++) a[i]=s[i]-'1';
    for (int i=0;i<n;i++) b[i]=a[i]%2;
    if (solve()){puts("1");return 0;}
    else {
        bool flag=0;
        for (int i=0;i<n;i++) flag|=(a[i]==1);
        if (flag) {puts("0");return 0;}
        for (int i=0;i<n;i++) b[i]=a[i]/2;
        if (solve()) puts("2"); else puts("0");
    }
    return 0;
}

### Prompt

Your challenge is to write 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;
const int maxn=1e6+3;
int n,a[maxn],b[maxn];
char s[maxn];
int solve(){
    int ret=0;
    for (int i=0;i<=n-1;i++) if ((i&(n-1))==i) ret^=b[i];
    return ret;
}
int main(){
    cin >> n >> s;
    for (int i=0;i<n;i++) a[i]=s[i]-'1';
    for (int i=0;i<n;i++) b[i]=a[i]%2;
    if (solve()){puts("1");return 0;}
    else {
        bool flag=0;
        for (int i=0;i<n;i++) flag|=(a[i]==1);
        if (flag) {puts("0");return 0;}
        for (int i=0;i<n;i++) b[i]=a[i]/2;
        if (solve()) puts("2"); else puts("0");
    }
    return 0;
}

```