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 (2.7.1) (judge verdict: Accepted)

n = gets.to_i
p = n.times.map do
  t, x, y = gets.split.map(&:to_i)
  { t: t, x: x, y: y }
end
p = p.unshift({ t: 0, x: 0, y: 0 })

def verify_move_amount(time_diff, prev_x, prev_y, current_x, current_y)
  moves = (current_x - prev_x).abs + (current_y - prev_y).abs
  return false if time_diff < moves
  return true if time_diff == moves
  (time_diff - moves).even?
end

possible = (1..p.length-1).all? do |i|
  prev = p[i-1]
  current = p[i]
  time_diff = current[:t] - prev[:t]
  verify_move_amount(time_diff, prev[:x], prev[:y], current[:x], current[:y])
end

puts possible ? 'Yes' : 'No'