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

Solution (in CPP):

Solution:
// Author: HarshKumar

#include <bits/stdc++.h>
using namespace std;
#define ll int64_t
const ll N = 1e6 + 6, M = 1e9 + 7;
int main()
{
    ios::sync_with_stdio(false), cin.tie(nullptr);
    ll n, ans = 1, r = 0, o = 0;
    string s;
    cin >> n >> s, n--;
    vector<ll> a(n);
    for (ll i = 0; i < n; i++)
        a[i] = abs(s[i] - s[i + 1]), o += a[i] == 1;
    if (!o)
    {
        ans *= 2;
        for (ll &e : a)
            e /= 2;
    }
    for (ll i = 0; i < n; i++)
        if (((n - 1) & i) == i)
            r ^= a[i];
    cout << (r % 2 ? ans : 0);
    return 0;
}