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>
using namespace std;
 
int main() {
  int N;
  cin >> N;
  string str;
  
  vector<int> numeral(N, 0);
  
  cin >> str;
  
  for (int i = 0; i < N; i++) {
    numeral.at(i) = (int)(str.at(i) - '0');
  }
  
  for (int i = 0; i < N - 1; i++) {
    for (int k = 0; k < N - i - 1; k++) {
      if (numeral.at(k) == 0) {
        numeral.at(k) = numeral.at(k + 1);
      }
      else if (numeral.at(k) == numeral.at(k + 1)) numeral.at(k) = 0;
      else if ((numeral.at(k) == 3 && numeral.at(k + 1) == 2) || (numeral.at(k) == 2 && numeral.at(k + 1) == 1) || (numeral.at(k) == 2 && numeral.at(k + 1) == 3) || (numeral.at(k) == 1 && numeral.at(k + 1) == 2)) {
        numeral.at(k) = 1;
      }
      else if ((numeral.at(k) == 3 && numeral.at(k + 1) == 1) || (numeral.at(k) == 1 && numeral.at(k + 1) == 3)) {
        numeral.at(k) = 2;
      }        
      /*else if (numeral.at(k) < numeral.at(k + 1) && numeral.at(k) != 0) {
        numeral.at(k) = numeral.at(k + 1) - numeral.at(k);
      }
      else if (numeral.at(k) != 0) {
        numeral.at(k) = numeral.at(k) - numeral.at(k + 1);
      }*/
    }
  }
  cout << numeral.at(0) << endl;
}