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.chomp.to_i
start = [0,0]
points = []
N.times do |i|
  points << gets.chomp.split(" ").map(&:to_i)
end
ans = ""
#元の位置に戻る方法 x+1 x-1, y+1 y-1,x+1 y+1 x-1 y-1,
points.each_with_index do |point,i|
  # point = [3,1,2]
  if i == 0

    if point[0] == point[1] + point[2]
      ans = "Yes"
    else
      ans = "No"
      break
  end
  else
    number = point[0] - points[i-1][0]
    x_move = points[i-1][1] - point[1]
    y_move = points[i-1][2] - point[2]
    if number == x_move + y_move
      ans = "Yes"
    elsif number > x_move + y_move
      if (number - x_move - y_move) % 2 == 0
        ans = "Yes"
      else
        ans = "No"
        break
      end
    else
      ans = "No"
      break
    end
  end
end

puts ans