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)

// inputに入力データ全体が入る
function Main(input) { 	
  	var args = input.split("\n");  	
  	var num = parseInt(args[0], 10); // 移動回数
  	var plan = []; // 移動計画
  	var position = [0, 0] // 自己位置
  	var judge = "";
  	
  	for(var i=1; i<args.length; i++){
      plan.push(args[i].split(" ").map(n => parseInt(n,10)))
    }
  
  	for(var i=0; i<plan.length; i++){
      	if(i!=0){
          	// 前回の時間を引いた数が今回の時間
			var t = plan[i][0] - plan[i-1][0];
        }else{
        	var t = plan[i][0]; 
        }
      	var x = plan[i][1];
      	var y = plan[i][2];
      
      	// 移動し時間を進める
   		if(i!=0){   
        	x_move = x-plan[i-1][1];
      		y_move = y-plan[i-1][2];
        }else{
        	x_move = x;
      		y_move = y;
        }
      	
      	// 移動量と時間の偶奇が一致したら可能
      	if( (x_move+y_move)<=t && (Math.abs(x_move)+Math.abs(y_move))%2 === t%2 ){
			judge = "Yes";         	 
        }else{
         	judge = "No" 
          	break;
        }
    }
  
  	console.log(judge);
}

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