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>
#define ll long long
#define ld long double
using namespace std;

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);

    int n;
    cin >> n;
    int arr[n];
    for (int i = 0; i < n; ++i) {
        char c;
        cin >> c;
        arr[i] = c - '0';
    }
    sort(arr, arr + n);
    int c1 = 0, c2 = 0, c3 = 0;
    for (int i = 0; i < n; ++i) {
        if(arr[i] == 1)
            c1++;
        else if(arr[i] == 2)
            c2++;
        else
            c3++;
    }
    // cout << c1 << c2 << c3 << "\n"; 
    if(c1 != 0 && c2 != 0 && c3 != 0){
        if(n >= 5)
            cout << 0 << "\n";
        else {
            if(c2 == 2)
                cout << 0 << "\n";
            else
                cout << 1 << "\n";
        }
    }
    else {
        if(c2 == 0) {
            if(c1 != c3)
                cout << 2 << "\n";
            else
                cout << 0 << "\n";
        }
        else{
            if(c1 == c2 || c3 == c2)
                cout << 0 << "\n";
            else
                cout << 1 << "\n";
        }
    }
    


    return 0;
}