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)

def action_handler(array, count)
  result = false
  current_nums = [0, 0, 0]
  time_index = 0
  x_index = 1
  y_index = 2
  for i in 0..(count - 1)
    is_first = i == 0
    is_last = i == (count - 1)
    if !is_last || (is_first && is_last)
      now_array = is_first ? current_nums : array[i]
      next_array = is_first ? array[i] : array[i + 1]
      dt = next_array[time_index] - now_array[time_index]
      dx = next_array[x_index] - now_array[x_index]
      dy = next_array[y_index] - now_array[y_index]
      #時間内に移動できるかの計算
      dxy = dx.abs + dy.abs
      if dxy <= dt
        new_dxy = dx + dy
        if dt.even? != new_dxy.even?
          return false
        else
          result = true
        end
      else
        return false
      end
    end
  end
  return result
end
=begin
def variable_finder(sec, coordinates)
  a = [coordinates[0] + 1, coordinates[1]]
  b = [coordinates[0] - 1, coordinates[1]]
  c = [coordinates[0], coordinates[1] + 1]
  d = [coordinates[0], coordinates[1] - 1]
  all_cases = [a, b, c, d]
  for x_i in 0..sec
    y_i = sec - x_i
    tmp = [coordinates[0] + x_i, coordinates[1] + y_i]
    tmp2 = [coordinates[0] - x_i, coordinates[1] + y_i]
    tmp3 = [coordinates[0] + x_i, coordinates[1] - y_i]
    tmp4 = [coordinates[0] - x_i, coordinates[1] - y_i]
    all_cases.push(tmp)
    all_cases.push(tmp2)
    all_cases.push(tmp3)
    all_cases.push(tmp4)
  end
  return all_cases.uniq
end
=end

#複数行に複数の要素が存在するとき
input = gets.chop.to_i
lines = []
while line = gets
    lines << line.chomp.split(' ').map(&:to_i)
end

#p action_handler([[3, 1, 2], [6, 1, 1]], 2) => true
print action_handler(lines, input) ? 'Yes' : 'No'