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

#define forn(i,n) for (int i = 0; i < int(n); i++)

const int N = 1e6 + 10;
int n, a[N];

int solve() {
    int ans = 0;
    for (int k = 0; k <= n; k++) {
        ans += ((k&(n-1)) == k) * a[k] % 2;
        ans %= 2;
    }
    return ans;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);

    bool one = 0;
    cin >> n; 
    string s; cin >> s;

    forn(i,n) {
        cin >> a[i];
        a[i] = s[i]-'0';
        one |= a[i] == 2;
    }

    int factor = one ? 1 : 2;
    forn(i,n) a[i] /= factor;

    cout << factor*solve() << endl;

    return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 forn(i,n) for (int i = 0; i < int(n); i++)

const int N = 1e6 + 10;
int n, a[N];

int solve() {
    int ans = 0;
    for (int k = 0; k <= n; k++) {
        ans += ((k&(n-1)) == k) * a[k] % 2;
        ans %= 2;
    }
    return ans;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);

    bool one = 0;
    cin >> n; 
    string s; cin >> s;

    forn(i,n) {
        cin >> a[i];
        a[i] = s[i]-'0';
        one |= a[i] == 2;
    }

    int factor = one ? 1 : 2;
    forn(i,n) a[i] /= factor;

    cout << factor*solve() << endl;

    return 0;
}

```