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>

using namespace std;

int n;
string s;
int a[1222333];

int main() {
	cin >> n;
	cin >> s;
	if (n == 1) {
		cout << s << "\n";
		return 0;
	}
	int f = 0;
	for (int i = 0; i+1 < n; i++) {
		a[i] = abs(s[i]-s[i+1]);
		if (a[i] == 1) f = 1;
	}
	if (f) {
		for (int i = 0; i < n-1; i++) {
			a[i] %= 2;
		}
	} else {
		for (int i = 0; i < n-1; i++) {
			a[i] /= 2;
		}
	}
	int x = 0;
	for (int i = 0; i < n-1; i++) {
		if (a[i] == 0) continue;
		if ((i|(n-2)) == n-2) x = 1-x;
	}
	if (!f) x *= 2;
	cout << x << "\n";
}