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)

#!/usr/bin/ruby

def travel(t, x, y, x_now, y_now)
  if t < (x - x_now).abs + (y - y_now).abs then
    return false
  elsif t == (x - x_now).abs + (y - y_now).abs then
    return true
  else
    return travel(t-2, x, y, x_now, y_now)
  end
end


t = [0]
x = [0]
y = [0]
i = 0

n = STDIN.gets.to_i

ret = true

while line = gets
  input = line.split(" ")
  t << input[0].to_i
  x << input[1].to_i
  y << input[2].to_i

  i += 1
  if i == n then
    break
  end
end

for i in 1..n do
  if !(travel(t[i]-t[i-1], x[i], y[i], x[i-1], y[i-1])) then
    ret = false
    break
  end
end

if ret then
  puts "Yes"
else
  puts "No"
end