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

#define for_(i,a,b) for(int i=a;i<b;++i)

bool is_odd(const vector<int>& v) {
    int n = v.size(), x = 0;
    for_(i,0,n) if (((n - 1) & i) == i) x ^= (v[i] & 1);
    return x;
}

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

    vector<int> v;
    for_(i,0,N) v.push_back(int(S[i] - '0') - 1);

    if (is_odd(v)) cout << 1 << endl;
    else if (find(v.begin(), v.end(), 1) != v.end()) cout << 0 << endl;
    else {
        for_(i,0,N) v[i] /= 2;
        if (is_odd(v)) cout << 2 << endl;
        else cout << 0 << endl;
    }
}
### Prompt

Your task is to create 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;

#define for_(i,a,b) for(int i=a;i<b;++i)

bool is_odd(const vector<int>& v) {
    int n = v.size(), x = 0;
    for_(i,0,n) if (((n - 1) & i) == i) x ^= (v[i] & 1);
    return x;
}

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

    vector<int> v;
    for_(i,0,N) v.push_back(int(S[i] - '0') - 1);

    if (is_odd(v)) cout << 1 << endl;
    else if (find(v.begin(), v.end(), 1) != v.end()) cout << 0 << endl;
    else {
        for_(i,0,N) v[i] /= 2;
        if (is_odd(v)) cout << 2 << endl;
        else cout << 0 << endl;
    }
}
```