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 (3.8.2) (judge verdict: Wrong Answer)

N = int(input())
txy = [list(map(int, input().split())) for i in range(N)]

txy = list(zip(*txy))

t = list(txy[0])
x = list(txy[1])
y = list(txy[2])
nowt = 0
nowx = 0
nowy = 0

for i in range(N):
    time = min(t)
    place = t.index(min(t))
    if time - nowt < abs(x[place]-nowx) + abs(y[place]-nowy):
        print("No")
        exit()
    elif ((time-nowt) - (abs(x[place]-nowx) + abs(y[place]-nowy)))%2 != 0:
        print("No")
        exit()
    else:
        nowt = time
        nowx = x[place]
        bowy = y[place]
        t[place] = 10**5 +1
        

print("Yes")