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++ (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define re register
inline int read(){
	re int t=0;
	re char v=getchar();
	while(v<'0')v=getchar();
	while(v>='0')t=(t<<3)+(t<<1)+v-48,v=getchar();
	return t;
}
int n,ans,a[1000002];
char s[1000002];

int main(){
	n=read();
	scanf("%s",s+1);
	if(n>30000){
for(re int i=1;i<100;++i){
			for(re int j=1;j<=n-i;++j)a[j]=abs(a[j]-a[j+1]);
		}printf("%d\n",a[1]);	}
	else{
		for(re int i=1;i<=n;++i)a[i]=s[i]-'0';
		for(re int i=1;i<n;++i){
			for(re int j=1;j<=n-i;++j)a[j]=abs(a[j]-a[j+1]);
		}
		printf("%d",a[1]);
	}
}