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 StoI(char i){
  if(i == '1'){
    return 1;
  }
  else if(i == '2'){
    return 2;
  }
  else if(i == '3'){
    return 3;
  }
}

int abs(int i){
  if(i < 0){
    return -1 * i;
  }
  else{
    return i;
  }
}
////////////////////////////////////メイン
int main() {
  int N;
  string S;
  cin >> N >> S;
  /*for(int i = 0;i < N;i++){
  	cin >> S.at(i);
  }*/
  vector<int> before(N);
  vector<int> after(N);
    
  for(int i = 0;i < N;i++){
    before.at(i) = StoI(S.at(i));
  }
  
  for(int i = 0;i < N-1;i++){
    
    for(int j = 0;j < N-1;j++){
		after.at(j) = abs( before.at(j) - before.at(j+1) );
          after.at(N -(1+i)) = 0;
    }
      for(int k = 0;k < N;k++){
        before.at(k) = after.at(k);
        //cout << before.at(k) << " ";
      }
  }
      
      ///////////////////////
 
  
  cout << after.at(0) << endl;
  
  
 
  //cout << answer << endl; // 5
}