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 (2.7.1) (judge verdict: Wrong Answer)

# n
# t x y

n = gets.to_i
t = []
x = []
y = []

t << 0
x << 0
y << 0
n.times do 
  t_temp, x_temp, y_temp = gets.split
  t << t_temp.to_i
  x << x_temp.to_i
  y << y_temp.to_i
end

def move_enable?(t_from, t_to, x_from, x_to, y_from, y_to)
  t_dif = t_to - t_from
  x_dif = x_to - x_from
  y_dif = y_to - y_from
  if t_dif < x_dif + y_dif
    return false
  elsif t_dif == x_dif + y_dif
    return true
  elsif ( t_dif - (x_dif + y_dif) ).even?
    return true
  else
    return false
  end
end

flag = "No"
n.times do |i|
  flag_temp = move_enable?(t[i], t[i+1], x[i], x[i+1], y[i], y[i+1])
  break unless flag_temp
  flag = "Yes" if i == n-1
end

puts flag