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 <iostream>
#include <vector>
#include <cmath>

using namespace std;

int main()
{
	int n; cin >> n;
	string s; cin >>s;
	vector<int> v(n);
	for(int i = 0; i < n; ++i)
		v[i] = s[i] - '0';

	int test = 100;
	while(test)
	{
		int num = 0;
		int zeroes = 0;
		int first = abs(v[0]-v[1]);
		int same = 0;
		
		for(int i = 0; i < n - 1; ++i)
		{
		
			v[i] = abs(v[i] - v[i+1]); 
			zeroes += (v[i] == 0);
			same += (v[i] == first);
			num = num ^ v[i];
			
		}
	
		if(zeroes == n-1)
		{
			cout << num;
			return 0;
		}
		if(same == n-1)
		{
			cout << num;
			return 0;
		}
		--n;
		--test;
	}
	cout << 2 ;
	return 0;
}