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: Accepted)

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

#define all(s) s.begin(), s.end()
#define pb push_back
#define ii pair<int, int>
#define x first
#define y second
#define bit(x, y) ((x >> y) & 1)
#define sz(s) ((int) (s).size())

const int N = 1000005;

int a[N];
int fac[N];

int v2C(int n, int k) {
    return fac[n] - fac[k] - fac[n - k];
}

int main() {
    ios::sync_with_stdio(false); cin.tie(0); 
    cout.tie(0);
    int n;
    cin >> n;
    string s;
    cin >> s;
    s = " " + s;
    bool check = 0;
    for (int i = 1; i <= n; i++) {
        a[i] = s[i] - '0' - 1;
        if (a[i] == 1) check = 1;
    }
    for (int i = 1; i <= n; i++) {
        int foo = i;
        fac[i] = fac[i - 1];
        while (foo % 2 == 0) {
            fac[i]++;
            foo /= 2;
        }
    }
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        if (v2C(n - 1, i - 1) == 0) {
            sum += a[i];
        }
    }
    if (sum % 2) return cout << 1, 0;
    if (check) return cout << 0, 0;
    sum = 0;
    for (int i = 1; i <= n; i++) {
        a[i] /= 2;
    }
    for (int i = 1; i <= n; i++) {
        if (v2C(n - 1, i - 1) == 0) {
            sum += a[i];
        }
    }
    if (sum % 2) cout << 2;
    else cout << 0;
    return 0;
}