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 12.16.1) (judge verdict: Accepted)

// inputに入力データ全体が入る
function Main(input) {
	// 1行目がinput[0], 2行目がinput[1], …に入る
	input = input.split("\n");
	cnt = input[0]-0;
	var t = [0];
	var x = [0];
	var y = [0];
	//文字列から10進数に変換するときはparseIntを使います
	var ret = "Yes";
	for (i=1; i<=cnt; i++)
	{
		tmp = input[i].split(" ");
		t.push(tmp[0]-0);
		x.push(tmp[1]-0);
		y.push(tmp[2]-0);
		if ( Math.abs(t[i-1]-t[i]) < Math.abs(x[i-1]-x[i]) + Math.abs(y[i-1]-y[i]) )
		{
			ret = "No";
			break;
		}
		if ( (Math.abs(t[i-1]-t[i]) - (Math.abs(x[i-1]-x[i]) + Math.abs(y[i-1]-y[i]))) % 2 != 0 )
		{
			ret = "No";
			break;
		}
	}
	//出力
	console.log('%s',ret);
}
//*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"));