Problem:
Score : 300 points

Problem Statement

AtCoDeer the deer is going on a trip in a two-dimensional plane.
In his plan, he will depart from point (0, 0) at time 0, then for each i between 1 and N (inclusive), he will visit point (x_i,y_i) at time t_i.

If AtCoDeer is at point (x, y) at time t, he can be at one of the following points at time t+1: (x+1,y), (x-1,y), (x,y+1) and (x,y-1).
Note that he cannot stay at his place.
Determine whether he can carry out his plan.

Constraints

1 ≤ N ≤ 10^5

0 ≤ x_i ≤ 10^5

0 ≤ y_i ≤ 10^5

1 ≤ t_i ≤ 10^5

t_i < t_{i+1} (1 ≤ i ≤ N-1)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
t_1 x_1 y_1
t_2 x_2 y_2
:
t_N x_N y_N

Output

If AtCoDeer can carry out his plan, print Yes; if he cannot, print No.

Sample Input 1

2
3 1 2
6 1 1

Sample Output 1

Yes

For example, he can travel as follows: (0,0), (0,1), (1,1), (1,2), (1,1), (1,0), then (1,1).

Sample Input 2

1
2 100 100

Sample Output 2

No

It is impossible to be at (100,100) two seconds after being at (0,0).

Sample Input 3

2
5 1 1
100 1 1

Sample Output 3

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
using namespace std;

int main() {
  int N, t, x, y;
  int a, b, c;
  bool result = true;
  cin >> N;
  
  vector<int> point;
  for (int i = 0; i < N; i++) {
      cin >> t >> x >> y;
      point.push_back(t);
      point.push_back(x);
      point.push_back(y);
  }

  int j = 0;
  for (int i = 0; i < N; i++) {
      a = i + j;
      b = i + j + 1;
      c = i + j + 2;
      cout << a << b << c;
      if ((point[a] - (point[b] + point[c])) % 2 != 0 || point[a] < (point[b] + point[c])) {
          result = false;
          cout << "No" << endl;
          break;
      }
      j = j + 2;
  }

  if (result) {
      cout << "Yes" << endl;
  }
  
}