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: Wrong Answer)

#include<cstdio>
#include<cstring>
inline int abs(const int x){return x<0?-x:x;}
int n,f[1000005],l;
char ch[1000005];
int main(){
	scanf("%d %s",&n,ch),l=strlen(ch)-1;
	for(int i=0;i<=l;++i)f[i]=ch[i]-'0';
	bool o[3]={0,0,1},num=false;
	for(int i=0;i<l;++i){
		f[i]=abs(f[i]-f[i+1]);
		if(f[i]==1)o[2]=0,o[1]^=1;
		if(f[i]==2)num^=1;
	}
	if(o[1]){putchar('1');return 0;}
	if(o[2] && num){putchar('2');return 0;}
	putchar('0');
	return 0;
}