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 8.8.3) (judge verdict: Accepted)

import Control.Monad
import Data.Array
import qualified Data.ByteString.Char8 as BS
import Data.Maybe

readInt = fromIntegral . fst . fromJust . BS.readInteger

readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine

getIntList = readIntList <$> BS.getLine

getIntNList n = map readIntList <$> replicateM (fromIntegral n) BS.getLine

checkI css tup 0 _ = True
checkI css tup n v
  | n == 3 = checkI css tup (n -1) diff
  | v == diff = checkI css tup (n -1) v
  | otherwise = False
  where
    diff = css ! (fst tup, n) - css ! (snd tup, n)

checkJ css tup 0 _ = True
checkJ css tup n v
  | n == 3 = checkJ css tup (n -1) diff
  | v == diff = checkJ css tup (n -1) v
  | otherwise = False
  where
    diff = css ! (n, fst tup) - css ! (n, snd tup)

main = do
  let num = 3
  css <- getIntNList num
  let css' = listArray ((1, 1), (num, num)) (concat css)
  if checkI css' (3, 2) 3 0 && checkI css' (2, 1) 3 0 && checkJ css' (3, 2) 3 0 && checkJ css' (2, 1) 3 0
    then putStrLn "Yes"
    else putStrLn "No"