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: Accepted)

-- ABC112 C - Pyramid
import Control.Monad
import Data.List

main :: IO ()
main = do
  n <- readLn
  am <- replicateM n $ map read . words <$> getLine :: IO [[Int]]
  putStrLn . unwords . map show $ solve am

solve :: [[Int]] -> [Int]
solve am = head . filter isOk $ [[x,y,centerH (x,y)] | x <- [0..100], y <- [0..100]]
  where
    isOk (cx:cy:ch:_) = all (\(x:y:h:_) -> height ch (x,y) (cx,cy) == h) am
    highest = last $ sortBy (\a b -> compare (a!!2) (b!!2)) am
    centerH = calcBackHeight highest

type Position = (Int, Int)
height :: Int -> Position -> Position -> Int
height h (x, y) (cx, cy) = max (h - (abs (x - cx)) - (abs (y - cy))) 0
calcBackHeight :: [Int] -> Position -> Int
calcBackHeight a (cx, cy) = h + (abs (x - cx)) + (abs (y - cy))
  where
    x = a !! 0
    y = a !! 1
    h = a !! 2