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)

N = gets.to_i

tn = []
xn = []
yn = []

N.times {
  t, x, y = gets.split.map(&:to_i)
  tn << t
  xn << x
  yn << y
}

t_prev = 0
x_prev = 0
y_prev = 0
(0..(N-1)).each { |i|
  t_next = tn[i]
  x_next = xn[i]
  y_next = yn[i]

  # 次の地点までの距離
  d = (x_next - x_prev).abs + (y_next - y_prev).abs

  # 移動に使える時間
  t = t_next - t_prev

  # 時間が足りないか、時間ちょうどにたどり着けない場合はアウト
  if t < d || (t - d) % 2 == 1
    puts "No"
    exit
  end

  t_prev = t_next
  x_prev = x_next
  y_prev = y_next
}

puts "Yes"