#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 1e6 + 10;

int N, A[MAX_N];

int main() {
    scanf("%d", &N);
    static char S[MAX_N]; scanf("%s", S + 1);
    for (int i = 1; i <= N; i++) A[i] = S[i] - '1';
    bool any_1 = false;
    for (int i = 1; i <= N; i++) if (A[i] == 1) any_1 = true;
    if (any_1)
        for (int i = 1; i <= N; i++) A[i] &= 1;
    else
        for (int i = 1; i <= N; i++) A[i] /= 2;
    int ans = 0;
    N--;
    for (int i = 0; i <= N; i++)
        if ((i & N) == i) ans ^= A[i + 1];
    printf("%d\n", ans * (any_1 ? 1 : 2));
}

### 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;

const int MAX_N = 1e6 + 10;

int N, A[MAX_N];

int main() {
    scanf("%d", &N);
    static char S[MAX_N]; scanf("%s", S + 1);
    for (int i = 1; i <= N; i++) A[i] = S[i] - '1';
    bool any_1 = false;
    for (int i = 1; i <= N; i++) if (A[i] == 1) any_1 = true;
    if (any_1)
        for (int i = 1; i <= N; i++) A[i] &= 1;
    else
        for (int i = 1; i <= N; i++) A[i] /= 2;
    int ans = 0;
    N--;
    for (int i = 0; i <= N; i++)
        if ((i & N) == i) ans ^= A[i + 1];
    printf("%d\n", ans * (any_1 ? 1 : 2));
}

```