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>
#include <string>
#define rep(i, n) for(i = 0; i < n; i++)
#define int long long

using namespace std;

const int N = 1e6 + 10;

int n;
int a[N];
int b[N];

signed main() {
	int i;
	
	cin >> n;
	string s; cin >> s;
	rep(i, n) {
		a[i] = s[i] - '1';
	}
	
	rep(i, n) {
		b[i] = a[i] % 2;
	}
	
	int hoge = 0;
	rep(i, n) {
		if (((n - 1) & i) == i) { hoge ^= b[i]; }
	}
	if (hoge == 1) { cout << 1 << endl; return 0; }
	
	rep(i, n) { if (a[i] == 1) break; }
	if (i < n) { cout << 0 << endl; return 0; }
	
	rep(i, n) {
		b[i] = a[i];
	}
	hoge = 0;
	rep(i, n) {
		if (((n - 1) & i) == i) { hoge ^= b[i]; }
	}
	cout << hoge << endl;
	return 0;
}