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";

const main = (arg) => {
  const input = arg.trim().split("\n");
  const N = parseInt(input[0]);
  // console.log(N);
  let currentX = 0;
  let currentY = 0;
  for (let i = 1; i < N + 1; i++) {
    let array = input[i].split(" ");
    let time = parseInt(array[0]);
    let x = parseInt(array[1]);
    let y = parseInt(array[2]);
    let moveX = x - currentX;
    let moveY = y - currentY;
    let totalMove = moveX + moveY;
    // ** 時間の総和を超えるとアウト
    if (time < totalMove) {
      console.log("No");
      break;
    }
    // ** time合計/奇数 * 移動の合計が奇数の場合OK
    if (
      (totalMove % 2 == 0 && time % 2 == 0) ||
      (totalMove % 2 != 0 && time % 2 != 0)
    ) {
      if (i == N) {
        console.log("Yes");
        break;
      }
    } else {
      console.log("No");
      break;
    }
  }
};
main(require("fs").readFileSync("/dev/stdin", "utf8"));
// https://atcoder.jp/contests/abc086/tasks/arc089_a