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"

func nextInt() int {
	var x int
	fmt.Scan(&x)
	return x
}

func abs(a int) int {
	if a > 0 {
		return a
	}
	return -a
}

func main() {
	N := nextInt()

	type whenWhere struct {
		t, x, y int
	}
	flgNG := false
	pre := whenWhere{0, 0, 0}
	for range make([]struct{}, N) {
		now := whenWhere{nextInt(), nextInt(), nextInt()}
		t := now.t - pre.t
		h := abs((now.x + now.y) - (pre.x + pre.y))

		if h > t || t%2 != h%2 {
			flgNG = true
		}
		pre = now
	}
	if !flgNG {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}

}