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::sync_with_stdio(false);
	cin.tie(nullptr);

	int n;
	cin >> n;

	string s;
	cin >> s;

	vector<int> a;
	a.resize(n);

	for(int i = 0; i < n; ++i) {
		a[i] = s[i] - '0' - 1;
	}

	bool one = false;

	for(int i = 0; i < n; ++i) {
		if(a[i] == 1) {
			one = true;
		}
	}

	if(one) {
		for(int i = 0; i < n; ++i) {
			a[i] %= 2;
		}
	}

	int ans = 0;

	for(int i = 0; i < n; ++i) {
		if(((n - 1) & i) == i) {
			ans ^= a[i];
		}
	}

	cout << ans << '\n';

	return 0;
}