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"
	"math"
)

func main() {
	var N int
	fmt.Scan(&N)
	T := make([]int, N + 1)
	X := make([]int, N + 1)
	Y := make([]int, N + 1)
	T[0] = 0
	X[0] = 0
	Y[0] = 0
	for i := 0; i < N; i++ {
		fmt.Scan(&T[i + 1], &X[i + 1], &Y[i + 1])
	}

	ans := true
	for i := 0; i < N; i++ {
		dt := float64(T[i + 1] - T[i])
		dist := math.Abs(float64(X[i + 1] - X[i])) + math.Abs(float64(Y[i + 1] - Y[i]))
		if dt < dist {
			ans = false
		}
		if int64(dist) % 2 != int64(dt) % 2.0 {
				ans = false
				}
	}
	if ans {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}