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>
#include <cstdio>
using namespace std;

int n, a[1000005];
string s;

int f() {
	int i, j, re=0;
	for(i=0; i<n; i++) {
		j = n - 1 - i;
		if((i^j) == i+j) re += a[i];
	}
	return re%2;
}

int main() {
	int i;
	cin >> n >> s;
	for(i=0; i<n; i++) a[i] = s[i] - '1';
	if(f()) return puts("1") * 0;
	for(i=0; i<n; i++) {
		if(a[i]==1) break;
		a[i] /= 2;
	}
	if(i<n) return puts("0") * 0;
	cout << f() * 2;
	return 0;
}