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: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var n int
	fmt.Scan(&n)
	var ti, xi, yi int
	var t [] int
	var x [] int
	var y [] int
	t = append(t,0)
	x = append(x,0)
	y = append(y,0)
	for i:=0 ; i<n; i++ {
	  fmt.Scanf("%d %d %d", &ti, &xi, &yi)
	  t = append(t,ti)
	  x = append(x,xi)
	  y = append(y,yi)
	}

	var dt,dx,dy int
	possible := true
	for i:=1; i<=n; i++ {
	  dt = t[i] - t[i-1]
	  dx = x[i] - x[i-1]
	  dy = y[i] - y[i-1]
	  if dt < (dx+dy) || (dt-(dx+dy))%2 == 1{
		possible = false
		break
	  }
	}
	if possible {
	  fmt.Println("YES")
	} else {
	  fmt.Println("NO")
	}
}