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 main
  integer, allocatable :: i(:, :)
  read (*, *) n
  allocate(i(3, 0:n))
  i(:, 0) = (/0, 0, 0/)
  read (*, *) i(:, 1:n)
  do k = 1, n
    jx = abs(i(2, k) - i(2, k - 1)) + abs(i(3, k) - i(3, k - 1))
    jt = i(1, k) - i(1, k - 1)
    if (jx > jt .or. ibits(jx, 0, 1) /= ibits(jt, 0, 1)) then
      write (*, *) "No"
      stop
    endif
  enddo
  write (*, *) "Yes"
end