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)

# coding: utf-8
"""this is python work script"""

def check_distance(trip_records):
    answer = True
    present_location = {'x':0, 'y':0}

    for d, x, y in trip_records:
        x_distance = abs(present_location['x'] - x)
        y_distance = abs(present_location['y'] - y)
        distance = x_distance + y_distance

        if d < distance:
            answer = False

        present_location['x'] = x
        present_location['y'] = y

    return answer


def check_parity(trip_records):
    answer = True

    for d, x, y in trip_records:
        if d % 2 != (x + y) % 2:
            answer = False
    return answer

def solver(trip_records):
    """solve this problem"""

    parity_ok = check_parity(trip_records)
    distance_ok = check_distance(trip_records)

    answer = 'No'
    if parity_ok and distance_ok:
        answer = 'Yes'

    return answer

def main():
    """main function"""
    N = int(input())
    trip_records = [list(map(int, input().rstrip().split(' '))) for _ in range(N)]

    answer = solver(trip_records)
    print(answer)

if __name__ == '__main__':
    main()