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>
#define MAXN 1000007
using namespace std;
int pb[MAXN],a[MAXN];
int main()
{
	int n;
	cin>>n;
	for(int i=0;i<n;i++) pb[i]=((i&(n-1))==i)?1:0;
	string s;
	cin>>s;
	for(int i=0;i<n;i++) a[i]=s[i]-'1';
	int p=0;
	for(int i=0;i<n;i++) p+=pb[i]*a[i];
	if(p&1) {printf("1"); return 0;}
	bool sp=true;
	for(int i=0;i<n;i++) if(a[i]&1) sp=false;
	if(!sp) {printf("0"); return 0;}
	int pn=0;
	for(int i=0;i<n;i++) pn+=pb[i]*(a[i]/2);
	if(pn&1) {printf("2"); return 0;}
	printf("0");
}