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 Python (3.4.3) (judge verdict: Accepted)

import sys
readline = sys.stdin.readline
N = int(readline())
t = []
x = []
y = []
for i in range(N):
    _t, _x, _y = list(map(int, readline().split()))
    t.append(_t)
    x.append(_x)
    y.append(_y)

p = [0, 0]
pt = 0
px = 0
py = 0
f = True
for i in range(N):
    a = t[i] - pt
    b = abs(px - x[i]) + abs(py - y[i])
    # 距離が足りないかt~t+1間の座標の差のと偶奇が一致しない場合はたどり着けない
    if a < b or (a % 2 != b % 2):
        f = False
        break
    px = x[i]
    py = y[i]
    pt = t[i]

if f == True:
    print('Yes')
else:
    print('No')