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: Accepted)

#include <stdio.h>
#include <algorithm>

using namespace std;

int main() {
  int n;
  scanf("%d", &n);

  int t[n+1], x[n+1], y[n+1];
  t[0] = 0;
  x[0] = 0;
  y[0] = 0;
  for (int i = 1; i < n+1; i++) {
    scanf("%d %d %d", t + i, x + i, y + i);
  }

  for (int i = 1; i < n+1; i++) {
    if ((x[i] - x[i-1]) + (y[i] - y[i-1]) > (t[i] - t[i-1]) || abs((x[i] - x[i-1]) + (y[i] - y[i-1]) - (t[i] - t[i-1])) % 2 != 0) {
      printf("No\n");

      return 0;
    }
  }

  printf("Yes\n");

  return 0;
}