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 Lua (5.3.2) (judge verdict: Accepted)

local math_abs = math.abs
local function distance(x1,y1,x2,y2)
    return math_abs(x1 - x2) + math_abs(y1 - y2)
end

local N = io.read("n")

local hints = {}
local hint_nonzero_x, hint_nonzero_y, hint_nonzero_h
for i=1,N do
    local x, y, h = io.read("n", "n", "n")
    hints[i] = {x, y, h}
    if h ~= 0 then
        hint_nonzero_x, hint_nonzero_y, hint_nonzero_h = x, y, h
    end
end

for cx=0,100 do
    for cy=0,100 do
        local h = hint_nonzero_h + distance(cx,cy,hint_nonzero_x,hint_nonzero_y)
        local ok = true
        for i=1,N do
            local hx, hy, hh = table.unpack(hints[i])
            if (h - distance(cx,cy,hx,hy) == hh) or
                (hh == 0 and h - distance(cx,cy,hx,hy) < 0)
            then
            else
                ok = false
                break
            end
        end
        if ok then
            print(table.concat({cx, cy, h}, ' '))
            return
        end
    end
end