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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List ( transpose )
import qualified Data.ByteString.Char8 as C
import Data.Maybe ( fromJust )

readInts :: IO [Int]
readInts = map (fst . fromJust . C.readInt) . C.words <$> C.getLine

main :: IO ()
main = do
  c1 <- readInts
  c2 <- readInts
  c3 <- readInts
  putStrLn $ if f c1 c2 c3 
               then "Yes"
               else "No"

f :: [Int] -> [Int] -> [Int] -> Bool
f c1 c2 c3 = let c = [c1,c2,c3] in
  yoko c && tate c

yoko, tate 
  :: [[Int]] -> Bool
yoko [c1@[c11,c12,c13], c2@[c21,c22,c23], c3@[c31,c32,c33]]
  = all (==c11-c21) (zipWith (-) c1 c2) &&
    all (==c21-c31) (zipWith (-) c2 c3) &&
    all (==c31-c11) (zipWith (-) c3 c1) 

tate = yoko . transpose