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)

# https://atcoder.jp/contests/abc086/tasks/arc089_a

Pos = Struct.new(:x, :y)

N = gets.to_i
ts = Array.new(N)
# xs = Array.new(N)
ps = Array.new(N) { Pos.new(0, 0) }
N.times do |i|
  ts[i], ps[i].x, ps[i].y = gets.split.map(&:to_i)
end

ts.insert(0, 0)
ps.insert(0, Pos.new(0, 0))

cond =  ps.zip(ts).each_cons(2).all? do |(p1, t1), (p2, t2)|
  d = (p1.x - p2.x).abs + (p1.y - p2.y).abs
  t = t2 - t1
  d <= t && (t - d).even?
end

puts cond ? 'Yes' : 'No'