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 N = parseInt(args,10);
	var history = args.slice(1,N+1);
	var answer;
	var flg = 1;
	for(var i=0;i<N-1;i++){
		var rec1 = parser(history[i]);
		var rec2 = parser(history[i+1]);
		var dt = rec2[0] - rec1[0];
		var dist = Math.abs(rec2[1]+rec2[2]-rec1[1]-rec1[2]);
		if (dt >= dist && dt % 2 === dist % 2){
		}else{
				flg = 0;
		}
	}
	answer = flg ? "Yes" : "No" ;
	//出力
	console.log(answer);
}
function parser(record){
	var args = record.split(" ");
	var return_val=[];
	return_val.push(parseInt(args[0],10));
	return_val.push(parseInt(args[1],10));
	return_val.push(parseInt(args[2],10));
	return return_val
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));