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<bits/stdc++.h>
using namespace std;
int main()
{
    int n;
    cin>>n;
    vector<int> arr(n+1);
    string my;
    cin>>my;
    int y =1;
    arr.push_back(0);
    for(char x : my)
    {
		int z = x-'0';
    	arr[y] = z;
		y++;
    }
  //  for(int i=1;i<=n;i++)
//	cout<<arr[i]<<" ";
//    cout<<endl<<endl;
    if(n==2)
    {
	cout<<abs(arr[2]-arr[1]);
	return 0;
    }
    int temp=n;
    vector<int> arr2(temp,0);
//    int ans = recfunc(n,1);
    for(int i=2;i<=n;i++)
    {
	
	//vector<int> arr2(temp);
	for(int j=1;j<=n-i+1;j++)
	    arr2[j]=abs(arr[j]-arr[j+1]);


//	for(int x : arr2)
//	    cout<<x<<" ";
//	cout<<endl;

	arr.resize(temp,0);
//	arr.clear();
	arr = arr2;
	--temp;
	if(i!=n);
	arr2.resize(temp,0);
//	arr2.c
//	cout<<arr2[1]<<endl;
    }
    cout<<arr2[1];
    return 0;
}