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)

const check = (t,d_x,d_y)=>{
  const xy = d_x+d_y;
  if (t<xy) return false;
  return t%2 === xy%2;
};
const travel = (plan)=>{
  'use strict';
  const current = [0,0,0];

  for (let d of plan) {
    const abs_x = Math.abs(current[1] - d[1]);
    const abs_y = Math.abs(current[2] - d[2]);
    const time = d[0] - current[0];

    if(!check(time,abs_x,abs_y)){return false}
    else{current[0] = d[0],current[1] = d[1],current[2] = d[2]}
  }

  return true

};
function Main(input) {
  const plan = input.split('\n').map(line=>line.split(' ').map(data=>parseInt(data))).slice(1);
  const result = travel(plan);
  console.log(result?'Yes':'No');
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));