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>

int main(){
    using namespace std;
    unsigned long N;
    cin >> N;
    string S;
    cin >> S;
    vector<unsigned long> a(N);
    map<unsigned long, unsigned long> m;
    transform(S.begin(), S.end(), a.begin(), [&m](char c){++m[c - 49]; return c - 49;});
    if(m.size() == 1)return 0 & puts("0");
    unsigned long c{1};
    if(m.size() == 2 && !m.count(1))c = 2;
    unsigned long p2{1};
    while(p2 < N)p2 <<= 1;
    p2 >>= 1;
    for(unsigned long lim{N}; p2; ){
        lim -= p2;
        for(unsigned long i{0}; i + p2 < N; ++i)a[i] ^= a[i + p2];
        while(p2 >= lim)p2 >>= 1;
    }
    cout << (a[0] & c) << endl;
    return 0;
}