// No.202525032120
#include <bits/stdc++.h>
#define N 1001000
using namespace std;

int n, a[N];

int main() {
#ifdef isLOCAL
    freopen(".in", "r", stdin);
    freopen(".out", "w", stdout);
#endif

    cin >> n;
    for (int i = 1; i <= n; ++i)
        scanf("%1d", a + i);

    for (int i = 1; i < n; ++i)
        a[i] = abs(a[i] - a[i + 1]);
    a[n] = 0;

    bool flag = 1;
    for (int i = 1; i < n; ++i)
        if (a[i] == 1) flag = 0;

    for (int i = 1; i < n; ++i)
        if (a[i] == 2) a[i] = flag;

    int ans = 0;
    for (int i = 0; i < n - 1; ++i)
        if (a[i + 1] == 1) ans ^= (((n - 2) & i) == i);

    if (ans) puts(flag ? "2" : "1");
    else puts("0");

    return 0;
}

### Prompt

Develop a solution in cpp 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
// No.202525032120
#include <bits/stdc++.h>
#define N 1001000
using namespace std;

int n, a[N];

int main() {
#ifdef isLOCAL
    freopen(".in", "r", stdin);
    freopen(".out", "w", stdout);
#endif

    cin >> n;
    for (int i = 1; i <= n; ++i)
        scanf("%1d", a + i);

    for (int i = 1; i < n; ++i)
        a[i] = abs(a[i] - a[i + 1]);
    a[n] = 0;

    bool flag = 1;
    for (int i = 1; i < n; ++i)
        if (a[i] == 1) flag = 0;

    for (int i = 1; i < n; ++i)
        if (a[i] == 2) a[i] = flag;

    int ans = 0;
    for (int i = 0; i < n - 1; ++i)
        if (a[i + 1] == 1) ans ^= (((n - 2) & i) == i);

    if (ans) puts(flag ? "2" : "1");
    else puts("0");

    return 0;
}

```