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

void f(int *d, int k, int c) {
    if(!k) {
        *d = 1;
        return;
    }
    while(!(k & c))
        c >>= 1;
    f(d + c, k ^ c, c >> 1);
    for(int i = 0; i <= (k ^ c); i++)
        d[i] = d[i + c];
}
int d[1111111];
int main() {
    int n;
    string a;
    cin >> n >> a;
    int t = 1;
    for(auto c : a)
        if(c == '2')
            t = 0;
    f(d, n - 1, 1 << 30);
    int r = 0;
    for(int i = 0; i < n; i++) {
        if(t && a[i] == '3')
            a[i] = '2';
        r ^= a[i] - '1' & d[i];
    }
    cout << (t ? r + r : r) << endl;
    return 0;
}

### Prompt

In CPP, your task is to solve 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;

void f(int *d, int k, int c) {
    if(!k) {
        *d = 1;
        return;
    }
    while(!(k & c))
        c >>= 1;
    f(d + c, k ^ c, c >> 1);
    for(int i = 0; i <= (k ^ c); i++)
        d[i] = d[i + c];
}
int d[1111111];
int main() {
    int n;
    string a;
    cin >> n >> a;
    int t = 1;
    for(auto c : a)
        if(c == '2')
            t = 0;
    f(d, n - 1, 1 << 30);
    int r = 0;
    for(int i = 0; i < n; i++) {
        if(t && a[i] == '3')
            a[i] = '2';
        r ^= a[i] - '1' & d[i];
    }
    cout << (t ? r + r : r) << endl;
    return 0;
}

```