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/).slice(1);
  input = input.map(v => v.split(/\s/).map(v => ~~v));

  let ans = "Yes"; // 'Yes' or 'No'
  let distance = 0;
  let time = 0;
  let nextPosi = { x: 0, y: 0 };
  let nextTime = 0;
  let tmpPosi = { x: 0, y: 0 };
  let tmpTime = 0;

  for (let i = 0; i < input.length; i++) {
    nextPosi.x = input[i][1];
    nextPosi.y = input[i][2];

    distance = Math.abs(nextPosi.x - tmpPosi.x + nextPosi.y - tmpPosi.y);

    nextTime = input[i][0];
    time = nextTime - tmpTime;
    if (distance > time || time % 2 != distance % 2) {
      ans = "No";
      break;
    }

    tmpTime = nextTime;
    tmpPosi.x = nextPosi.x;
    tmpPosi.y = nextPosi.y;
  }

  console.log(ans);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));