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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <iomanip>
#include <algorithm>
#include <utility>
#include <cmath>
#include <string>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <deque>
#include <numeric>


using namespace std;

using ll = long long;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define mkp(a, b) make_pair(a, b)

int main() {
	int n;
	cin >> n;
	string s;
	cin >> s;
	vector<int> b(n - 1);
	rep(i, n - 1) {
		b[i] = abs(s[i] - s[i + 1]);
	}

	while(b.size() > 1) {
		for (int bb : b) {
			cout << bb;
		}
		cout << endl;
		vector<int> c;
		bool is_first = true;
		rep(i, b.size() - 1) {
			int cur = abs(b[i] - b[i + 1]);
			if (is_first && cur == 0) {
				continue;
			}
			is_first = false;
			c.push_back(cur);
		}
		int last_index = ((int) c.size()) - 1;
		for (int i = 1; i < c.size(); i++) {
			if (c[i] != 0) {

				last_index = i;
			}
		} 
		vector<int> d;
		for (int i = 0; i <= last_index; i++) {
			d.push_back(c[i]);
		} 
		b = d;


	}
	if (b.size() == 1) {
		cout << b[0] << endl;
	} else {
		cout << 0 << endl;		
	}

	return 0;
}