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: Accepted)

#!/usr/bin/env ruby

# time, x, y

plans = []

gets.to_i.times do
  t, x, y = gets.split
  plans << [t.to_i, x.to_i, y.to_i]
end

def is_reachable(t, dist_x, dist_y)
  rest_time = t - (dist_x + dist_y)
  return false if rest_time < 0
  return false if rest_time % 2 != 0
  return true
end

pos = [0, 0]
now = 0

res = true

plans.each do |plan|
  dist_t = plan[0] - now
  dist_x = (pos[0] - plan[1]).abs
  dist_y = (pos[1] - plan[2]).abs

  unless is_reachable(dist_t, dist_x, dist_y) then
    res = false
    break
  end

  now = plan[0]
  pos = [plan[1], plan[2]]
end

puts res ? "Yes" : "No"