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())
txy_init = [[0, 0, 0]]
txy = txy_init + [[int(i) for i in input().split(" ")] for i in range(N)]
t, x, y = 0, 1, 2

checker = True
for i in range(N):
    dt = txy[i+1][t] - txy[i][t]
    dxy = abs(txy[i+1][x] - txy[i][x]) + abs(txy[i+1][y] - txy[i][y])
    
    if dt < dxy:
        checker = False
    else:
        if (dt - dxy) % 2 == 0:
            continue
        else:
            checker = False
    
    if checker:
        continue
    else:
        break

if checker:
    print("Yes")
else:
    print("No")