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: Runtime Error)

# O(n^2)
# { x + y + z = N
# { 10000x + 5000y + 1000z = Y
n = gets.to_i
$plan = []
n.times do
  $plan << gets.chomp.split(" ").map(&:to_i)
end

$i = 0
$flag = Array.new(n,false)

def solve(t,x,y,i)

#  puts "now: t:#{t} x:#{x} y:#{y}"

  if t > $plan.last[0]
    return false
  end

  if t > $plan[i][0] && $flag[i] == false
    puts "No"
    exit
  end
  
  if $plan[i][0] == t
    if $plan[i][1] == x && $plan[i][2] == y
      $flag[i] = true
      i += 1
    else
      return false
    end
  end

  solve(t+1,x+1,y,i)
  solve(t+1,x-1,y,i)
  solve(t+1,x,y+1,i)
  solve(t+1,x,y-1,i)

end

solve(0,0,0,0)
#p $flag
if $flag.all?
  puts "Yes"
else
  puts "No"
end