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() {
	int N;
	string A;
	cin >> N >> A;
	vector<int> aa(N);
	bool exist1 = false;
	for (int i = 0; i < N; ++ i) {
		aa[i] = A[i]-'1';
		if (aa[i] == 1) exist1 = true;
	}

	vector<int> a;
	for (int i = 0; i < N; ++ i) {
		if ((i | (N-1-i)) == N-1) a.push_back(i);
	}

	if (exist1) {
		int r = 0;
		for (auto i : a) {
			r ^= aa[i]&1;
		}
		cout << r << endl;
	} else {
		int r = 0;
		for (auto i : a) {
			r ^= aa[i];
		}
		cout << r << endl;
	}
}