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) {
  const args = input.split('\n'); // args = ["2", "3 1 2", "6 1 1"]
  const N = parseInt(args[0], 10); // N = 2
  const nums = args.slice(1, N + 1); // nums = ["3 1 2", "6 1 1"]

  const isValid = nums.every((n) => {

    var ns = n.split(' '); // ns = ["3", "1", "2"]
    var t = parseInt(ns[0], 10), // t = 3
      x = parseInt(ns[1], 10), // x = 1
      y = parseInt(ns[2], 10); // y = 2
    var sum = x + y;

    return (t >= sum) && ((t % 2) === (sum % 2));
  });

  if (isValid) {
    console.log('Yes');
  } else {
    console.log('No');
  }
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));