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

func dist(x0, y0, x1, y1 int) int {
	return abs(x0-x1) + abs(y0-y1)
}

func main() {
	var n int
	fmt.Scan(&n)
	ts := make([]int, n+1)
	xs := make([]int, n+1)
	ys := make([]int, n+1)
	ts[0] = 0
	xs[0] = 0
	ys[0] = 0
	for i := 1; i < n+1; i++ {
		fmt.Scan(&ts[i], &xs[i], &ys[i])
	}

	for i := 0; i < n; i++ {
		dist := dist(xs[i], ys[i], xs[i+1], ys[i+1])
		dt := ts[i+1] - ts[i]
		if dist > dt || (dt-dist)%2 != 0 {
			fmt.Println("No")
			return
		}
	}
	fmt.Println("Yes")
}