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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

type piramid
    x :: Int
    y :: Int
    h :: Int
end 

function main()
N = parseInt(readline())
piramids = []
for _ in 1:N
    x,y,h = parseMap(split(readline()))
    push!(piramids,piramid(x,y,h))
end

piramids = sort(collect(piramids), by=x->x.h)

for X in 0:100
    for Y in 0:100
        ok = 0 
        kizyun_piramid =  piramids[1]
        kizyun_h = kizyun_piramid.h + abs(kizyun_piramid.x - X) + abs(kizyun_piramid.y - Y)
        for i in 1:N
            piramid = piramids[i]
            if piramid.h != 0
                H = piramid.h + abs(piramid.x - X) + abs(piramid.y - Y)
                if kizyun_h == H
                    ok += 1
                end
            else
                return 100000000000000
                h_max = abs(piramid.x - X) + abs(Y - piramid.y)
                if H <= h_max
                    ok += 1
                end    
            end    
        end    
        if ok == N && kizyun_h >= 1
            return "$X $Y $kizyun_h"
        end
    end
end
end

println(main())