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: Wrong Answer)

# 入力値の取得
n = gets.chomp.to_i
points = n.times.map { |i|
  point_array = gets.chomp.split(" ").map(&:to_i)
  { t: point_array[0], x: point_array[1], y: point_array[2] }
}

# 計算
def canMove(current, dist)
end

current = { t: 0, x: 0, y: 0 }
goal = true

points.each do |point|
  dt = point[:t] - current[:t]
  dx = (point[:x] - current[:x]).abs
  dy = (point[:y] - current[:y]).abs
  dxy = dx + dy

  if dt > 0 && dxy <= dt && dt.even? ? dxy.even? : dxy.odd?
    current = point
    next
  end

  goal = false
  break
end

puts goal ? "YES" : "NO"