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: Accepted)

import sys
N = int(input())
t=[0]*(N+1)
x=[0]*(N+1)
y=[0]*(N+1)
#距離を保管する変数
dist = 0
#時間の差を保管しておくための変数
dt = 0 
#初期値を保管しておく
now_x =0
now_y =0

t[0] = 0
x[0] = now_x
y[0] = now_y
for i in range(1,N+1):
    t[i],x[i],y[i] = map(int, input().split())
    
for i in range(1,N+1):    
    #距離を計算する
    dist = abs(x[i]-x[i-1])+abs(y[i]-y[i-1])
    dt = abs(t[i] - t[i-1])
    #時間が足りないときは絶対にいけない
    if(dist > dt):
        print('No')
        sys.exit()
    else:
        #dtが偶数なら、進む距離も偶数なはず
        #その逆も然り
        if(dt %2 != dist %2):
            print('No')
            sys.exit()
    
print('Yes')