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 (3.8.2) (judge verdict: Accepted)

#!/user/bin/env pypy3
import sys
from typing import NamedTuple, List


def fast_input():
    return sys.stdin.readline()[:-1]


class Position(NamedTuple):
    t: int
    x: int
    y: int

    def _calc_diff_move(self, position) -> int:
        diff_x = self.x - position.x
        diff_y = self.y - position.y
        return abs(diff_x) + abs(diff_y)

    def can_move_from(self, prev) -> bool:
        diff_t = self.t - prev.t
        diff_move = self._calc_diff_move(prev)
        if not diff_t % 2 == diff_move % 2:
            return False
        return diff_t >= diff_move


def result_format(b: bool) -> str:
    return "Yes" if b else "No"


def solve(positions: List[Position]) -> bool:
    positions = [Position(t=0, x=0, y=0)] + positions
    for p_ind in range(len(positions) - 1):
        p_curr = positions[p_ind]
        p_next = positions[p_ind + 1]
        if not p_next.can_move_from(p_curr):
            return False
    return True


def main():
    n = int(fast_input())
    positions = []
    for _ in range(n):
        t, x, y = list(map(int, fast_input().split()))
        positions.append(Position(t=t, x=x, y=y))
    result = solve(positions)
    print(result_format(result))


main()