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)

require 'pp'

N,d=gets.chomp.split(' ').map{|n| n.to_i}
x_0 = 0
y_0 = 0
t_0 = 0
noflg = false
i=1
while(i<=N)
	t,x_t,y_t=gets.chomp.split(' ').map{|n| n.to_i}
	x_d = x_t - x_0
	y_d = y_t - y_0
	t_d = t   - t_0
	sum_d = x_d + y_d
	if(sum_d > t_d || ((t_d)-(sum_d)) % 2 != 0)
		noflg = true
		break
	end
	x_0 = x_t
	y_0 = y_t
	t_0 = t
	i+=1
end
if(noflg)
	puts "No"
else
	puts "Yes"
end