Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program probC
  implicit none
  integer :: c(3,3),a(3),b(3)
  integer i,j,k,ans

  do i=1,3
     read(*,*) c(i,1:3)
  end do

  do i=0,100
     ans=0
     a(1)=i

     b(1)=c(1,1)-a(1)
     b(2)=c(1,2)-a(1)
     b(3)=c(1,3)-a(1)
     
     a(2)=c(2,1)-b(1)
     a(3)=c(3,1)-b(1)

     do j=1,3
        do k=1,3
           if(c(j,k).ne.a(j)+b(k)) ans=1
        end do
     end do

     if(ans==0) then
        write(*,*) 'Yes'
        stop
     end if
  end do

  write(*,*) 'No'
  
end program probC