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)

n = int(input())
G=[None for i in range(n)]
res = True

def dps(d):
    global res
    P=[0,0,0]   #Pはt,x,yのリスト
    for i in range(d):
        if G[i] != None:
            gt,gx,gy = G[i]
            pt,px, py = P
            if (gt-pt) >= (gx-px + gy-py):
                if (gt-pt - (gx-px + gy-py))%2 == 0:
                    res &=  True
                else:
                    res = False
                    break
            else:
                res = False
                break
            P=G[i]
        else:
            res &= True
            
    

for i in range(n):
    t,x,y = map(int,input().split())
    if G[i]==None:
        G[i] = []
        G[i].append(t)
        G[i].append(x)
        G[i].append(y)
        dps(i+1)
    elif G[i]==[t,x,y]:
        dps(i+1)
    else:
        res == False
        break
    if res == False:
        break

        
print('Yes' if res==True else 'No')