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)

class AtCoDeer:
    def __init__(self):
        self.pos = {"x": 0, "y": 0}
        self.time = 0

    def move(self, to_x, to_y):
        self.pos = {"x": to_x, "y": to_y}
        return self.pos

    def can_move(self, t, to_x, to_y):
        dx = abs(to_x-self.pos.get("x"))
        dy = abs(to_y-self.pos.get("y"))
        total_move = dx + dy
        dt = t - self.time

        if dt < total_move:
            return False
        elif (dt-total_move) % 2 != 0:
            return False
        else:
            self.move(to_x, to_y)
            self.time = t
            return True


def main():
    n = int(input()) - 1
    at_co_deer = AtCoDeer()

    while(at_co_deer.can_move(*[int(x) for x in input().split()])):
        if n <= 0:
            break
        elif n > 0:
            n -= 1
    
    # 計画破綻判明後のデータ読み捨て
    for i in range(n):
        input()

    if n == 0:
        print("Yes")
    else:
        print("No")

if __name__ == "__main__":
    main()