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 Control.Applicative 
import Data.Char
import Debug.Trace
import Data.List

splitInt :: String -> [Integer]
splitInt "" = [] :: [Integer]
splitInt str =
    let charToInt :: Integer -> Char -> Integer
        charToInt d c = d * 10 + (fromIntegral $ digitToInt c) :: Integer
        checkInt :: Integer -> String -> (Integer, String)
        checkInt d "" = (d, "")
        checkInt d (' ':rest) = (d, rest)
        checkInt d (c:rest) = checkInt (charToInt d c)  rest
        (num, rest) = checkInt 0 str
        in num : splitInt rest

check :: [[Integer]] -> Bool
check [[aa, ab, ac], [ba, bb, bc], [ca, cb, cc]] = 
    let z = ((aa - ab) == (ba - bb)) && ((aa - ab) == (ca - cb))
        y = ((aa - ac) == (ba - bc)) && ((aa - ac) == (ca - cc))
        x = ((ab - ac) == (bb - bc)) && ((ab - ac) == (cb - cc))
        w = ((aa - ba) == (ab - bb)) && ((aa - ba) == (ac - bc))
        v = ((ba - ca) == (bb - cb)) && ((ba - ca) == (bc - cc))
        u = ((ca - aa) == (cb - ab)) && ((ca - aa) == (cc - ac))
        in z && y && x && w && v && u

getMat :: Int -> IO [[Integer]]
getMat 0 = return [] :: IO [[Integer]]
getMat n = (:) <$> (splitInt <$> getLine) <*> getMat (n - 1)

main = do
    a <- check <$> getMat 3
    putStrLn (if a then "Yes" else "No")