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)

lines = $stdin.read
array = lines.split("\n")

N   = array[0].to_i
ans = true

pos  = [0,0]
before_time = 0

array[1..N+1].each_with_index do |str,i|

  next_time, next_x, next_y = str.split(" ").map(&:to_i)
  dist_x = [pos.first, next_x].max - [pos.first, next_x].min
  dist_y = [pos.last , next_y].max - [pos.last,  next_y].min
  dist = dist_x + dist_y
  time = next_time - before_time

  puts "s[#{pos.first},#{pos.last}]=>d[#{next_x},#{next_y}] = dist #{dist} with time = #{time}"

  if time < dist
    puts "No"
    exit 0
  elsif time == dist
    # just in time
    pos,before_time = [next_x, next_y],next_time
    next
  elsif i+1 == N and time >= dist
    next
  else
    # time > dist
    rest = time - dist
    if rest % 2 == 0
      pos = [next_x, next_y]
      next
    else
      puts "No"
      exit 0
    end
  end
end

puts "Yes"