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 val[1000003] , N; char str[1000003];

int main(){
	scanf("%d %s" , &N , str + 1); bool flg = 1;
	for(int i = 1 ; i < N ; ++i) flg &= (val[i] = abs(str[i] - str[i + 1])) != 1;
	if(flg) for(int i = 1 ; i < N ; ++i) val[i] >>= 1;
	int sum = 0; for(int i = 1 ; i < N ; ++i) sum ^= (((N - 2) & (i - 1)) == i - 1) & val[i];
	cout << (sum << flg); return 0;
}