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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";

function Main(input) {
  input = input.split("\n");
  const N = input.shift();
  let x = 0;
  let y = 0;
  for (let i = 0; i < N; i++) {
    let row = input[i].split(" ");
    let flag = false;
    quit: for (let n = 0; n < row[0]; n++) {
      for (let m = 0; m < row[0]; m++) {
        if (
          (n == row[1] && m == row[2] && (row[0] - n + m) % 2 == 0) ||
          (x - n == row[1] && y - m == row[2] && (row[0] - n + m) % 2 == 0)
        ) {
          x = n;
          y = m;
          flag = true;
          break quit;
        }
      }
    }
    if (flag == false) {
      console.log("No");
      return;
    }
  }
  console.log("Yes");
}

Main(require("fs").readFileSync("/dev/stdin", "utf-8"));