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: Runtime Error)


# 整数の入力
n = gets.to_i
# point[0]に、「t = 0のとき点(0, 0)にいる」という情報を持たせる
point = []
point[0] = [0, 0, 0]
# スペース区切りの整数の入力
for i in 1..n do
  point[i] = gets.chomp.split.map(&:to_i);
end


# 出力を仮に"Yes"とする
ans = true

# シカのAtCoDeerくんが訪れた地点の間の距離と所要時間について検証
n-1.times do |j|
  # ある時刻から、次の時刻までの時間（== 総移動距離）
  actual_t = point[j+1][0] - point[j][0]
  # ある時刻の座標と、次の時刻の座標の間の「X軸方向の距離 + Y軸方向の距離」
  min_t = (point[j+1][1] - point[j][1]).abs + (point[j+1][2] - point[j][2]).abs
  # もし「その時間でその距離は移動できない」か「求めた２つの値の差が奇数」なら
  if actual_t < min_t || (actual_t - min_t).odd?
    ans = false
    break
  end
end

puts ans ? "Yes" : "No"