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: Time Limit Exceeded)

# -*- coding:utf-8 -*-
if __name__ == "__main__":
    N = int(input())
    dic = {}
    queue = [(0,0)]
    time = 0
    maxTime = float('-inf')
    flag = True
    for tmp in range(N):
        t, x, y = map(int, input().split())
        dic[t] = (x, y)
        maxTime = max(maxTime, t)

    while time < maxTime and flag:
        time += 1
        factor = []

        for tmp in queue:
            x = tmp[0]
            y = tmp[1]
            if time in dic:
                if dic[time] == (x+1,y) or dic[time] == (x-1,y) or dic[time] == (x,y+1) or dic[time] == (x,y-1):
                    factor.append(dic[time])
            else:
                factor.append((x+1,y))
                factor.append((x-1,y))
                factor.append((x,y+1))
                factor.append((x,y-1))
        else:
            factor = list(set(factor))

        if time in dic and len(factor) == 0:
            flag = False

        queue = factor
    else:
        if flag:
            print("Yes")
        else:
            print("No")