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>
#include <string>
#include <algorithm>    
#include <cmath>
#include <map>
#include <vector>
#include <math.h>
#include <stdio.h>
#include <stack>
#include <queue>
#include <tuple>
#include <cassert>
#include <set>
#include <functional>
#define int long long
#define mod(int)(1000000007)
using namespace std;
int test[3456789];
signed main() {
	int n, m, ans = 0; string s; cin >> n >> s;
	for (int h = 0; h < n; h++) {
		test[h] = (int)(s[h]);
	}
	if (n * n - 1 / 2 <= 1000000000000) {
		int a = n - 1;
		for (int h = 0; h < n - 1; h++) {
			for (int i = 0; i < a; i++) {
				test[i] = abs(test[i] - test[i + 1]);
			}
		}
		cout << test[0] << endl;
	}
	else {
		cout << abs((int)(s[0]) - (int)(s[n - 1])) << endl;
	}
	return 0;
}