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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int		abs(int n)
{
	if (n < 0)
		n *= -1;
	return (n);
}

int		main()
{
	int		N;
	char	*row;
	int		i;

	scanf("%d\n", &N);
	row = (char *)malloc(sizeof(char) * (N + 1));
	while (i < N)
	{
		if ((i + 1) < N)
			scanf("%c ", &row[i]);
		else
			scanf("%c\n", &row[i]);
		row[i] -= '0';
		i++;
	}
	while (N)
	{
		N--;
		i = 0;
		while (i < N)
		{
			row[i] -= row[i + 1];
			row[i] = abs(row[i]);
			i++;
		}
	}
	printf("%d\n", row[0]);
	return (0);
}