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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define ll long long int
#define ld long double
#define pb push_back
#define pf push_front
#define ft first
#define sc second
#define all(v) v.begin(), v.end()
using namespace std;
const int maxn = 3000;
signed main() {
    ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    int n;
    cin >> n;
    vector<pair<int, int> > vec(n, {0, 1});
    for (int d = 0; d < n; d++) {
        char c;
        cin >> c;
        vec[d].ft = c - '0';
    }
    while (vec.size() > 1) {
        vector<pair<int, int> > vec1;
        vec1.pb({vec[0].ft, vec[0].sc});
        for(int d = 1; d < vec.size(); d++) {
            if (vec1.back().ft != vec[d].ft) {
                vec1.pb({vec[d].ft, vec[d].sc});
            } else {
                vec1.back().sc += vec[d].sc;
            }
        }
        for (int d = 0; d < vec1.size(); d++) {
            if (vec1[d].ft == 0) {
                vec1[d].sc = min(vec1[d].sc, 1);
            }
        }
        vec.clear();
        for (int d = 1; d < vec1.size(); d++) {
            if (vec1[d - 1].sc > 1) {
                vec.pb({0, vec1[d-1].sc - 1});
            }
                vec.pb({abs(vec1[d].ft - vec1[d - 1].ft), 1});
        }
        if (vec1.back().sc > 1) {
            vec.pb({0, vec1.back().sc - 1});
        }
        for (int d = 0; d < vec.size(); d++) {
            if (vec[d].ft == 0) {
                vec[d].sc = min(vec[d].sc, 1);
            }
        }
//        for (int d = 0; d < vec.size(); d++) {
//            cout << vec[d].ft << " " << vec[d].sc << "\n";
//        }
//        cout <<'\n';
    }
    if (vec[0].sc > 1) {
        cout << 0;
    } else {
        cout << vec[0].ft;
    }


}