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;
	assert(N >= 2);
	string A; cin >> A;

	N--; // number of iterations instead

	int ans2 = 0;
	for (int i = 0; i <= N; i++) {
		if ((N & i) == i) {
			ans2 += A[i]; ans2 %= 2;
		}
	}

	if (ans2) {
		cout << 1 << '\n';
		exit(0);
	} else {
		int ans4 = 0;
		for (int i = 0; i <= N; i++) {
			if (A[i] == '2') {
				cout << 0 << '\n';
				exit(0);
			}
			if ((N & i) == i) {
				ans4 += A[i]-1; ans4 %= 4;
			}
		}
		cout << ans4 << '\n';
	}

	return 0;
}