Problem:
Score: 300 points

Problem Statement

In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.

The pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0).

Aoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information:

C_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1.

Additionally, he obtained N pieces of information. The i-th of them is: "the altitude of point (x_i, y_i) is h_i."

This was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.

Constraints

N is an integer between 1 and 100 (inclusive).

x_i and y_i are integers between 0 and 100 (inclusive).

h_i is an integer between 0 and 10^9 (inclusive).

The N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.

The center coordinates and the height of the pyramid can be uniquely identified.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1 h_1
x_2 y_2 h_2
x_3 y_3 h_3
:
x_N y_N h_N

Output

Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.

Sample Input 1

4
2 3 5
2 1 5
1 2 5
3 2 5

Sample Output 1

2 2 6

In this case, the center coordinates and the height can be identified as (2, 2) and 6.

Sample Input 2

2
0 0 100
1 1 98

Sample Output 2

0 0 100

In this case, the center coordinates and the height can be identified as (0, 0) and 100.

Note that C_X and C_Y are known to be integers between 0 and 100.

Sample Input 3

3
99 1 191
100 1 192
99 0 192

Sample Output 3

100 0 193

In this case, the center coordinates and the height can be identified as (100, 0) and 193.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as B
import Control.Monad
import Data.Char

toTriple :: B.ByteString -> (Int, Int, Int)
toTriple bs =
    let
        Just (a, bs') = B.readInt bs
        Just (b, bs'') = B.readInt $ B.dropWhile isSpace bs'
        Just (c, _) = B.readInt $ B.dropWhile isSpace bs''
    in
        (a, b, c)

f :: (Int, Int, Int) -> (Int, Int) -> Int
f (x,y,h) (cx,cy) = (abs $ cx - x) + (abs $ cy - y) + h

main = do
    n <- readLn :: IO Int
    xyh <- replicateM n (toTriple <$> B.getLine) :: IO [(Int, Int, Int)]
    forM_ [0..100] $ \i ->
        forM_ [0..100] $ \j -> do
            let xs = filter (/=0) $ map (flip f (i,j)) xyh
            unless (null xs) $ do
                let k = head xs
                let res = and $ map (\(x,y,h) -> (max (k-(abs$i-x)-(abs$j-y)) 0) == h) xyh
                when res $ do
                    putStr $ show i ++ " "
                    putStr $ show j ++ " "
                    putStrLn $ show k