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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'pry'

plan = [{t: 0, x: 0, y: 0}]
gets.to_i.times do
  input = gets.split(' ').map(&:to_i)
  plan += [{ t: input[0], x: input[1], y: input[2] }]
end

ans = nil

(plan.size - 1).times do |i|
  time = plan[i + 1][:t] - plan[i][:t]
  x_distance = (plan[i + 1][:x] - plan[i][:x]).abs
  y_distance = (plan[i + 1][:y] - plan[i][:y]).abs
  if (x_distance + y_distance <= time) && ((x_distance + y_distance) % 2 == time % 2)
    ans = 'YES'
  else
    ans = 'NO'
    break
  end
end

puts ans