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

int comb(int n, int r){
    return n == (r | (n-r));
}

int main(){
    int N;
    string S;
    cin >> N >> S;

    vector<int> A(N);
    for(int i=0; i<N; i++) A[i] = S[i] - '1';

    int num[3] = {0};
    for(int a : A) num[a]++;
    if(num[1]){
        int res = 0;
        for(int i=0; i<N; i++){
            res += A[i] * comb(N-1, i);
            res %= 2;
        }
        cout << res << endl;
    }else{
        for(int& a : A) a /= 2;
        int res = 0;
        for(int i=0; i<N; i++){
            res += A[i] * comb(N-1, i);
            res %= 2;
        }
        cout << res*2 << endl;
    }

    return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 comb(int n, int r){
    return n == (r | (n-r));
}

int main(){
    int N;
    string S;
    cin >> N >> S;

    vector<int> A(N);
    for(int i=0; i<N; i++) A[i] = S[i] - '1';

    int num[3] = {0};
    for(int a : A) num[a]++;
    if(num[1]){
        int res = 0;
        for(int i=0; i<N; i++){
            res += A[i] * comb(N-1, i);
            res %= 2;
        }
        cout << res << endl;
    }else{
        for(int& a : A) a /= 2;
        int res = 0;
        for(int i=0; i<N; i++){
            res += A[i] * comb(N-1, i);
            res %= 2;
        }
        cout << res*2 << endl;
    }

    return 0;
}

```