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>
#define ll long long
#define endl "\n"
using namespace std;

void solve(){
	ll n;
	cin>>n;
	ll a[n];
	ll g;
	cin>>g;
	for(ll i=0; i<n; ++i){
		ll temp = g%10;
		a[i] = temp;
		g = g/10;
		
	}
	ll x=0,ans=0;
	ll count=0;
	ll end = n-1;
	while(end != 0){
		
		for(ll i=0; i<end; ++i){
			if(end == 1){
				count = abs(a[i] - a[i+1]);
				break;
			}
			a[i] = abs(a[i] - a[i+1]);
			// cout<<a[i]<<" ";
			
		}
		// cout<<endl;
		end--;
	}
	
	cout<<count<<endl;

}

int main(){
	// freopen("input.txt", "r",stdin);
	// freopen("output.txt", "w", stdout);
	int t=1;
	// cin>>t;
	while(t--){
		solve();
	}
	return 0;
}