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 <iostream>
#define MAXN 1000000
using namespace std;
int main(){
	int N;
	char a[MAXN];
	cin >> N >> a;
	bool has2 = 0;
	int ans = 0, coeff = 0;
	for(int i=0; i<N; i++){
		a[i] -= '0';
		has2 += (a[i] == 2);
	}
	if(!has2)
		for(int i=0; i<N; i++)
			a[i] /= 2;
	for(int i=1; i<=N; i++){
		ans += coeff? 0:a[i-1];
		coeff += __builtin_ctz(N-i) - __builtin_ctz(i);
	}
	cout << ((ans % 2)? 2-has2:0) << endl;
}