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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

type Position struct {
	Time, X, Y int
}

func main() {
	var n int
	fmt.Scan(&n)

	schedule := make([]Position, n)
	for i := 0; i < n; i++ {
		var time, x, y int
		fmt.Scan(&time, &x, &y)
		schedule[i] = Position{Time: time, X: x, Y: y}
	}

	res := true
	position := Position{Time: 0, X: 0, Y: 0}

	for i := 0; i < len(schedule); i++ {
		destination := schedule[i]

		// 移動
		for j := position.Time + 1; j <= destination.Time; j++ {
			position.Time = j
			if position.X != destination.X {
				if position.X < destination.X {
					position.X++
				} else {
					position.X--
				}
			} else if position.Y != destination.Y {
				if position.Y < destination.Y {
					position.Y++
				} else {
					position.Y--
				}
			} else {
				position.X++
			}
		}

		if position.X != destination.X || position.Y != destination.Y {
			res = false
			break
		}
	}

	if res {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}