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 (gfortran v4.8.4) (judge verdict: Accepted)

program probC
  implicit none
  integer*8,allocatable :: t(:),x(:),y(:)
  integer*8 N,i,del_x,del_y,del_t,del_min

  read(*,*) N
  allocate(t(0:N),x(0:N),y(0:N))
  t=0
  x=0
  y=0
  do i=1,n
     read(*,*) t(i),x(i),y(i)
  end do
  
  do i=1,N
     del_t=t(i)-t(i-1)
     del_x=x(i)-x(i-1)
     del_y=y(i)-y(i-1)
     del_min=del_t-abs(del_x)-abs(del_y)
     select case(del_min)
     case(:(-1))
        write(*,*) 'No'
        stop
     end select
     select case(mod(del_min,2))
     case(1)
        write(*,*) 'No'
        stop
     end select
  end do

  write(*,*) 'Yes'
end program probC