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 Java8 (OpenJDK 1.8.0) (judge verdict: Memory Limit Exceeded)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		// スペース区切りの整数の入力
		int st, sx, sy, et, ex, ey;
		et = 0;
		ex = 0;
		ey = 0;
		for (int i = 0; i < n; i++) {
			st = et;
			sx = ex;
			sy = ey;

			et = sc.nextInt();
			ex = sc.nextInt();
			ey = sc.nextInt();

			if (!can(et - st, ex - sx, ey - sy)) {
				System.out.println("No");
				return;
			}
		}
		System.out.println("Yes");
	}

	public static int fixZero = 1000;
	public static int[][][] ans = new int[fixZero][2 * fixZero][2 * fixZero];

	public static boolean can(int t, int x, int y) {
		if (t == 0) {
			if (x == 0 && y == 0) {
				return true;
			} else {
				return false;
			}
		}
		if (!(t < fixZero && Math.abs(x) < fixZero && Math.abs(y) < fixZero)) {
			return can(t - 1, x - 1, y) || can(t - 1, x + 1, y) || can(t - 1, x, y - 1) || can(t - 1, x, y + 1);
		}
		if (ans[t][x + fixZero][y + fixZero] == 1) {
			return true;
		} else if (ans[t][x + fixZero][y + fixZero] == 2) {
			return false;
		} else {
			boolean b = can(t - 1, x - 1, y) || can(t - 1, x + 1, y) || can(t - 1, x, y - 1) || can(t - 1, x, y + 1);
			if (b) {
				ans[t][x + fixZero][y + fixZero] = 1;
			} else {
				ans[t][x + fixZero][y + fixZero] = 2;
			}
			return b;
		}
	}
}