Problem:
Score : 700 points

Problem Statement

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}.

Sample Input 1

4
1231

Sample Output 1

1

x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

Sample Input 2

10
2311312312

Sample Output 2

0

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define STDIO
#define MOD 1000000007
#define testbit(mask,i) (((mask)>>(i))&1)
#define setbit(mask,i) ((mask)|(1<<i))
#define delbit(mask,i) ((mask)^(1<<i))
#define lowbit(x) ((x)&(-x))
#define INF MOD
using namespace std;
int n;
int a[1000100];
int mod2(int n,int k){
	k=(k|(n-k));
	if(n==k)
		return 3;
	return 0;
}
void End(int pp){
	printf("%d\n",pp);
	exit(0);
}
int main(){
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%1d",&a[i]);
		a[i]--;
	}
	int x=0,y=0;
	for(int i=0;i<n;i++){
		x^=(mod2(n-1,i)&a[i]);
		y|=a[i];
	}
	if(x&1)
		End(1);
	else if(y&1)
		End(0);
	else if(x&2)
		End(2);
	else
		End(0);
	return 0;
}