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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import math


# Me
class Check():
    def __init__(self):
        self.now_t, self.now_x, self.now_y = 0, 0, 0

    def do(self, t, x, y):
        distance = math.sqrt((x - self.now_x) * (y - self.now_y))
        duration = t - self.now_t
        if duration < distance:
            return False

        if (t - self.now_t) % 2 != (x + y - (self.now_x + self.now_y)) % 2:
            return False
        self.now_t, self.now_x, self.now_y = t, x, y
        return True


N = int(input())
c = Check()
for i in range(N):
    a = [int(x) for x in input().split()]
    if not c.do(a[0], a[1], a[2]):
        print('No')
        exit()
print('Yes')