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

#define MAX_N 1000006
#define LOG_N 20

int twos[MAX_N] ,lg2[MAX_N];

int main()
{
    for(int i=0; i<LOG_N; i++)
        lg2[1<<i] = i;
    for(int i=1; i<MAX_N; i++)
        twos[i] += twos[i-1] + lg2[i&-i];

    int n;
    string s;
    cin >> n >> s;

    if(count(s.begin() ,s.end() ,'2') == 0){
        bool on = 0;
        for(int i=0; i<n; i++)
            on ^= (s[i] == '3')&!(twos[n-1]-twos[n-i-1]-twos[i]);
        cout << 2*on << endl;
    }
    else{
        bool on = 0;
        for(int i=0; i<n; i++)
            on ^= !(s[i]&1)&!(twos[n-1]-twos[n-i-1]-twos[i]);
        cout << on << endl;
    }
}