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)

program sample
    implicit none
  
    integer(8) :: i,j,m,n,a,b,t,a0,b0,t0
    integer(8),allocatable :: x(:),y(:)
  
    read(*,*) n
    a0=0
    b0=0
    t0=0
    do i=1,n
        read(*,*)t,a,b
        m=abs(a-a0)+abs(b-b0)
        if (m>t-t0)then
            write(*,*)'No'
            stop
        elseif(mod(m,2)/=mod(t-t0,2))then
            write(*,*)'No'
            stop
        end if
        a0=a
        b0=b
        t0=t
    end do


  
    write(*,*) 'Yes'
  
    stop
end program sample