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: Wrong Answer)

      PROGRAM traveling
      IMPLICIT NONE
      INTEGER :: N
      INTEGER,ALLOCATABLE :: t(:), x(:),y(:)
      
      INTEGER :: i, dt, dx,dy, s
      LOGICAL :: flag = .TRUE.
      
      READ*,N
      N = N + 1
      ALLOCATE( t(N),x(N),y(N) )
      DO i = 2,N
        READ*,t(i),x(i),y(i)
      END DO
      t(1) = 0
      x(1) = 0
      y(1) = 0
      
      DO i = 1,N-1
        dt = t(i+1) - t(i)
        dx = abs( x(i+1)-x(i) )
        dy = abs( y(i+1)-y(i) )
        
        IF(dx+dy>dt)THEN
          flag = .false.
          EXIT
        END IF
        
        s = dy+dx -dt
        IF( mod(dx+dy,2)/=mod(dt,2) )THEN
          flag = .false.
          EXIT
        END IF
      END DO
      
      IF(flag)THEN
        print'(A)','YES'
      ELSE
        print'(A)','NO'
      END IF
      
      
      END PROGRAM