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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

row_length = int(input())
point = {}
for i in range(row_length):
    point[i] = list(map(int, input().split()))
from math import ceil
def feasible_point(t, x, y):
    if t % 2 == 0:  # tが偶数の時
        k = t / 2
        # (x,y)がk * kの間にある偶数点ならばokを返す
        if ((x+y)%2 == 0)&(x <= k)&(y <= k):
            return True
        else:
            return False
    else:
        k = ceil(t / 2)
        # (x,y)がk * kの間にある奇数点ならばokを返す
        if ((x+y)%2 == 1)&(x <= k)&(y <= k):
            return True
        else:
            return False

check_list = []
for j in range(len(point)):
    check_list.append(feasible_point(point[j][0], point[j][1], point[j][2]))

if all(check_list):
    # 各点同士の両立可能性を調べる
    check_list_2 = []
    for l in range(len(point)-1):
        t_gap = point[l+1][0] - point[l][0]
        xy_gap = point[l+1][1] + point[l+1][2] - point[l][1] - point[l][2]
        if xy_gap <= t_gap:
            check_list_2.append(True)
        else:
            check_list_2.append(False)
    if all(check_list_2):
        print("Yes")
    else:
        print("No")
else:
    print("No")