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: Time Limit Exceeded)

N = int(input())
pre_t = 0
pre_x = 0
pre_y = 0
count = 0
for _ in range(N):
    flag = False
    t, x, y = map(int, input().split())
    for a in range(t - pre_t + 1):
        for b in range(t- pre_t + 1 - a):
            for c in range(t - pre_t + 1  - a - b):
                d = t - pre_t - a - b - c
                if pre_x + a - b == x and pre_y + c - d == y:
                    count += 1
                    flag = True
                    break
            if flag:
                break
        if flag:
            break
    pre_t = t
    pre_x = x
    pre_y = y
if count == N:
    print("Yes")
else:
    print("No")