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)

// ABC086

// inputに入力データ全体が入る
function Main(input) {
  input = input.split("\n");
  const N = parseInt(input[0],10);
  var result = "Yes";
  var x = 0;
  var y = 0;
  var beforeT = 0;
  for(var i=1;i<=N+1;i++) {
    // 所有時間
    var t = parseInt(input[i].split(" ")[0],10) - beforeT;

    // 次の目的地
    var nextX = parseInt(input[i].split(" ")[1],10);
    var nextY = parseInt(input[i].split(" ")[2],10);

    // 次の目的地までの距離
    var xSubscration = subtractionGoal(x,nextX);
    var ySubscration = subtractionGoal(y,nextY);
    var totalSubscration = xSubscration + ySubscration;

    // 時間が足りない場合
    if(totalSubscration > t) {
      result = "No";
      // 時間が余ったが、余った時間を持て余せない場合
    } else if(totalSubscration < t && (t - totalSubscration) %2 != 0) {
      result = "No";
    }
    x = nextX;
    y = nextY;
    beforeT = t;
  }
  console.log(result);
}

function subtractionGoal(s,nextS) {
  var num = 0;
  if(s > nextS) {
    num = s - nextS;
  } else {
    num = nextS - s;
  }
  return num;
}

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