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


int solve(vector<int> arr)
{
    int N = arr.size();
    bool flag = false, a0 = true;
    for(int i=0; i<N; ++i)
    {
        if(arr[i] == 1) flag = true;
        if(arr[i] != 0) a0 = false;
    }
    if(a0) return 0;
    if(!flag)
    {
        for(int i=0; i<N; ++i) arr[i] /= 2;
        return 2*solve(arr);
    }
    int ans = 0;
    for(int i=0; i<=N-1; ++i)
        if( ((N-1)&i) == i ) ans ^= arr[i]&1;
    return ans;
}

int main()
{
    int N; scanf("%d", &N);
    vector<int> arr;
    for(int i=0; i<N; ++i)
    {
        int t;
        scanf("%1d", &t);
        arr.push_back(t-1);
    }
    printf("%d\n", solve(arr));
}
### Prompt

Please create a solution in CPP 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;


int solve(vector<int> arr)
{
    int N = arr.size();
    bool flag = false, a0 = true;
    for(int i=0; i<N; ++i)
    {
        if(arr[i] == 1) flag = true;
        if(arr[i] != 0) a0 = false;
    }
    if(a0) return 0;
    if(!flag)
    {
        for(int i=0; i<N; ++i) arr[i] /= 2;
        return 2*solve(arr);
    }
    int ans = 0;
    for(int i=0; i<=N-1; ++i)
        if( ((N-1)&i) == i ) ans ^= arr[i]&1;
    return ans;
}

int main()
{
    int N; scanf("%d", &N);
    vector<int> arr;
    for(int i=0; i<N; ++i)
    {
        int t;
        scanf("%1d", &t);
        arr.push_back(t-1);
    }
    printf("%d\n", solve(arr));
}
```