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;

int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n;
	cin >> n;
	string s;
	cin >> s;
	vector<int> a(n);
	for(int i = 0; i < n; i++) a[i] = s[i] - '1';
	bool has1 = false;
	for(int i = 0; i < n; i++){
		if(a[i] == 1) has1 = true;
	}
	if(!has1){
		for(int i = 0; i < n; i++){
			a[i] /= 2;
		}
	}
	int ans = 0;
	for(int i = 0; i < n; i++){
		int j = (n-1) - i;
		if((i ^ j) == (i + j)){
			ans += a[i];
			ans %= 2;
		}
	}
	if(!has1) ans *= 2;
	cout << ans << '\n';
}