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)

// g++ -std=c++17 b.cpp -o a.out && ./a.out < in
#include <iostream>
#include <algorithm>
#include <math.h>
#include <string>
#include <map>
#define ll long long
#define IOS cin.sync_with_stdio(false);cin.tie(nullptr);
#define endl "\n"
#define pb push_back
#define rep(t, n) for (int t=0;t<(n);++t)
const ll NN = 1e5+5;
using namespace std;

int main() {
    IOS;
    int n;
    string s, ss;
    cin >> n >> s;
    int dp[n+2];

    reverse(s.begin(), s.end());
    dp[0] = abs(s[0] - s[1]);
    for (int t=1;t<n-1;++t) {
        dp[t] = abs(s[t] - s[t+1]);
        dp[t] -= dp[t-1];
    }
    cout << dp[n-1];
}