#include <bits/stdc++.h>
using namespace std;

int main(){
    int n;
    vector<int> one, two;
    string s;
    bool flg = true;
    cin >> n >> s;
    --n;
    for(int i=0;i<=n;++i){
        int d = s[i] - '1';
        one.emplace_back(d & 1);
        two.emplace_back(d == 2);
        if(d & 1) flg = false;
    }
    int ans = 0;
    for(int i=0;i<=n;++i){
        if((n&i) == i) ans += one[i];
    }
    if(ans & 1){ cout << 1 << endl; return 0; }
    if(!flg){ cout << 0 << endl; return 0; }
    ans = 0;
    for(int i=0;i<=n;++i){
        if((n&i) == i) ans += two[i];
    }
    if(ans & 1){ cout << 2 << endl; return 0; }
    cout << 0 << endl;

    return 0;
}
### Prompt

In cpp, your task is to solve 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;

int main(){
    int n;
    vector<int> one, two;
    string s;
    bool flg = true;
    cin >> n >> s;
    --n;
    for(int i=0;i<=n;++i){
        int d = s[i] - '1';
        one.emplace_back(d & 1);
        two.emplace_back(d == 2);
        if(d & 1) flg = false;
    }
    int ans = 0;
    for(int i=0;i<=n;++i){
        if((n&i) == i) ans += one[i];
    }
    if(ans & 1){ cout << 1 << endl; return 0; }
    if(!flg){ cout << 0 << endl; return 0; }
    ans = 0;
    for(int i=0;i<=n;++i){
        if((n&i) == i) ans += two[i];
    }
    if(ans & 1){ cout << 2 << endl; return 0; }
    cout << 0 << endl;

    return 0;
}
```