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: Wrong Answer)

N = int(input())

t = [0] * N
x = [0] * N
y = [0] * N

for i in range(N):
    t[i],x[i],y[i] = map(int,input().split())

boolian = True    

if N == 1:
    delta_t = t[0]
    delta_x = x[0]
    delta_y = y[0]
    
    delta_sum = delta_x + delta_y
    k = delta_sum % 2 
    j = delta_t % 2
    
    if -delta_t < delta_sum and delta_sum < delta_t:
        if k == 0 and j == 0:
            boolian = True
        if k == 1 and j == 1:
            boolian = True
        else:
            boolian = False
            print('No')
    else:
        boolian = False
        print('No')
        
if N > 1:
    for i in range(N-1):

        delta_t = t[i+1] - t[i]
        delta_x = x[i+1] - x[i]
        delta_y = y[i+1] - y[i]

        delta_sum = delta_x + delta_y
        k = delta_sum % 2 
        j = delta_t % 2

        if -delta_t < delta_sum and delta_sum < delta_t:
            if k == 0 and j == 0:
                boolian = True
            if k == 1 and j == 1:
                boolian = True
            else:
                boolian = False
                print('No')
        else:
            boolian = False
            print('No')


if boolian == True:
    print('Yes')