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: Time Limit Exceeded)

#include<iostream>
using namespace std;
int math(char n)
{
	if(n=='1')
	return 1;
		if(n=='2')
	return 2;
		if(n=='3')
	return 3;
		if(n=='4')
	return 4;
		if(n=='5')
	return 5;	
	if(n=='6')
	return 6;
		if(n=='7')
	return 7;
		if(n=='8')
	return 8;
		if(n=='9')
	return 9;
		if(n=='0')
	return 0;
}
int match(int m,int n)
{
	int d;
	if(m>=n)
	d=m-n;
	else
	d=n-m;
	return d;
}
int main()
{
	char a[1000005];
	int n,i,j,m,b[1000005];
	cin>>n;
	for(i=1;i<=n;i++)
	{
		cin>>a[i];
		b[i]=math(a[i]);
	}
	m=n;
	for(i=1;i<n;i++)
	{
		m=n-i;
		for(j=1;j<=m;j++)
		{
		b[j]=match(b[j],b[j+1]);
		}
	}
	
	cout<<b[1]<<endl;

 }