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: Wrong Answer)

N = int(input())
list = [[int(i) for i in input().split()] for i in range(N)]
list.insert(0, [0, 0, 0])

if N == 1:
    timeInterval = list[1][0] - list[0][0]
    distance = abs(list[1][1]+list[1][2]-list[0][1]-list[0][2])
    if timeInterval < distance:
        print("No")
    elif (timeInterval - distance)%2 == 0:
        print("Yes")
    else:
        print("No")
else:
    for i in range(N):
        timeInterval = list[i+1][0] - list[i][0]
        distance = abs(list[i+1][1]+list[i+1][2]-list[i][1]-list[i][2])
        if timeInterval < distance:
            if i == N-1:
                print("No")
        elif (timeInterval - distance)%2 == 0:
            if i == N-1:
                print("Yes")
        else:
            if i == N-1:
                print("No")