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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int main() {
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int N; cin >> N;
	assert(N >= 2);
	string A; cin >> A;

	N--; // number of iterations instead

	int ans2 = 0;
	for (int i = 0; i <= N; i++) {
		if ((N & i) == i) {
			ans2 += A[i]; ans2 %= 2;
		}
	}

	if (ans2) {
		cout << 1 << '\n';
		exit(0);
	} else {
		int ans4 = 0;
		for (int i = 0; i <= N; i++) {
			if (A[i] == 1) {
				cout << 0 << '\n';
				exit(0);
			}
			if ((N & i) == i) {
				ans4 += A[i]; ans4 %= 4;
			}
		}
		cout << ans4 << '\n';
	}

	return 0;
}