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 tenquestionten
 integer,allocatable,dimension(:) :: X
 integer,allocatable,dimension(:) :: Y
 integer,allocatable,dimension(:) :: T
 integer N, i, j, sum, Xl, Yl, Tl, Z
 read(*,*) N
 allocate(X(N+1))
 allocate(Y(N+1))
 allocate(T(N+1))
 sum=0
 X(1) = 0
 Y(1) = 0
 T(1) = 0
  do i=2,N+1
  read(*,*) T(i), X(i), Y(i)
  end do
  do i=1,N
  Xl=abs(X(i+1)-X(i))
  Yl=abs(Y(i+1)-Y(i))
  Tl=abs(T(i+1)-T(i))
  Z=Xl+Yl
   if (Z.ge.Tl) then
    if ((mod(Z,2)).eq.(mod(Tl,2))) then
    sum = sum + 1
    end if
   end if
  end do
 if (sum.eq.N-1) then
 write(*,*) "YES"
 else if (sum.ne.N-1) then
 write(*,*) "NO"
 end if
end program