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<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long LL;
const int _=1e2;
const int maxn=1e6+_;

char ss[maxn];
int len[2],d[2][maxn],c[2][maxn];
inline int myabs(int x){return x>0?x:-x;}
int main()
{
	int n,w=0;
	scanf("%d%s",&n,ss+1);
	d[w][len[w]=1]=ss[1]-'0',c[w][len[w]]=1;
	for(int i=2;i<=n;i++)
		if(ss[i]==ss[i-1])c[w][len[w]]++;
		else d[w][++len[w]]=ss[i]-'0',c[w][len[w]]=1;
	
	for(int t=1;t<n;t++)
	{
		len[w^1]=0;d[w^1][0]=-1;
		for(int i=1;i<=len[w];i++)
		{
			int dd=0,cc=c[w][i]-1;
			if(cc!=0)
			{
				if(d[w^1][len[w^1]]==dd)c[w^1][len[w^1]]+=cc;
				else d[w^1][++len[w^1]]=dd,c[w^1][len[w^1]]=cc;
			}
			if(i!=len[w])
			{
				int dd=myabs(d[w][i]-d[w][i+1]),cc=1;
				if(d[w^1][len[w^1]]==dd)c[w^1][len[w^1]]+=cc;
				else d[w^1][++len[w^1]]=dd,c[w^1][len[w^1]]=cc;
			}
		}
		w^=1;
	}
	printf("%d\n",d[w][len[w]]);

	return 0;
}