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 _GLIBCXX_DEBUG
#define INF 100000000
using namespace std;
const int mod = 1000000007;


char itoc(int i) {
    if (i == 0)return '0';
    else if (i == 1)return '1';
    else if (i == 2)return '2';
    else return '3';

}
int ctoi(char c) {
    if (c >= '0' && c <= '9') {
        return c - '0';
    }
    return 0;
}

char getNext(char& x, char& y) {
    return itoc(abs(ctoi(x) - ctoi(y)));
}

int main() {

    int N;
    cin >> N;
    string a, b = "";
    cin >> a;
    while (true) {
        for (int i = 0; i < a.size() - 1; i++) {
            char k = getNext(a[i], a[i+1]);
            if(k!='0'||i==0)b.push_back(k);
        }
        if (b.size() <= 1)break;
        a = b;
        b = "";
    }
    if (b.size() == 1)cout << ctoi(b[0]) << endl;
    else cout << 0 << endl;
}