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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

implicit none
integer:: n,i
integer,allocatable:: t(:),x(:),y(:),ta(:),xa(:),ya(:)
 
read(*,*) n
allocate(t(n))
allocate(x(n))
allocate(y(n))
allocate(ta(n))
allocate(xa(n))
allocate(ya(n))
do i=1,n
read(*,*) t(i),x(i),y(i)
end do
ta(1)=t(1)
xa(1)=x(1)
ya(1)=y(1)
do i=2,n
ta(i)=abs(t(i)-t(i-1))
xa(i)=abs(x(i)-x(i-1))
ya(i)=abs(y(i)-y(i-1))
end do
 
do i=1,n
if(ta(i)<xa(i)+ya(i).or.mod(ta(i),2)/=mod(xa(i)+ya(i),2))then
write(*,*) 'No'
goto 100
endif
end do
 
write(*,*) 'Yes'
 
100 end