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)


N = int(input())

# x, y
start = [0, 0]

def get_tile(x, y):
    if x%2 == 0:
        if y %2 == 0: return 0
        else: return 1
    else:
        if y %2 == 0: return 1
        else: return 0


for i in range(N):
    t, x, y = map(int, input().split())
    tile_start = get_tile(start[0], start[1])
    tile_now = get_tile(x, y)

    if t % 2 == 0:
        if tile_start != tile_now:
            print('No')
            exit()
    else:
        if tile_start == tile_now:
            print('No')
            exit()

    if abs(x-start[0]) + abs(y-start[1]) > t:
        print('No')
        exit()

print('Yes')