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;
typedef long long ll;
typedef vector<int> vi;
vi w;
int main() {
	int n;
	cin >> n;
	string s;
	cin >> s;
	bool on = false;
	for(int i=0;i<n;i++) {
		int val = s[i]-'1';
		w.push_back(val);
		on = on || (val == 1);
	}
	int cho = n-1;
	int res = 0;
	if(on) {
		for(int i=0;i<n;i++) {
			if((w[i] == 1) && ((i & cho) == i)) {
				res ^= 1;
			}
		}
	} else {
		for(int i=0;i<n;i++) {
			if((w[i] == 2) && ((i & cho) == i)) {
				res ^= 2;
			}
		}
	}
	cout << res << '\n';
}