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;

#define ll long long
#define ar array

const int mxN=1e6;
int n;
string s;

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> n >> s;
	int s1=0;
	for(int i=0; i<n; ++i)
		if((i&n-1)==i)
			s1+=s[i]-1-'0';
	if(s1&1) {
		cout << 1;
		return 0;
	}
	for(int i=0; i<n; ++i) {
		if(s[i]=='2') {
			cout << 0;
			return 0;
		}
	}
	int s2=0;
	for(int i=0; i<n; ++i)
		if((i&n-1)==i)
			s2+=(s[i]-1-'0')/2;
	if(s2&1)
		cout << 2;
	else
		cout << 0;
}