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)

import Data.List
import Text.Printf
nextPyramid (x,y) = if y+1<101 then (x,y+1) else if x+1<101 then (x+1,0) else (-1,-1)
listToTuple [x,y,z] = (x,y,z)

check::(Integer,Integer)->[(Integer,Integer,Integer)]->Integer->Integer
check (x,y) (d:ds) h
    | h==0      = check (x,y) ds (abs (a-x) + abs (b-y) + c)
    | c==tmp    = if ds==[] then h else check (x,y) ds h
    | otherwise = -1
    where
        (a,b,c) = d
        tmp     = max (h - abs (a-x) - abs (b-y)) 0

solve (x,y) tbl
    | ans == -1 = solve (nextPyramid (x,y)) tbl
    | otherwise = (x,y,ans)
    where
        ans     = check (x,y) tbl 0

main::IO()
main=do
    getLine
    tbl <- map (listToTuple.map read.words) . lines <$> getContents :: IO [(Integer,Integer,Integer)]
    let (x,y,h) = solve (0,0) (sortBy (\(a0,a1,a2) (b0,b1,b2) -> compare b2 a2) tbl)
    printf "%d %d %d\n" x y h