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)

function input()
  local inp = io.read()
  local r={}
  string.gsub(inp,"(%S+)", function (v) table.insert(r,tonumber(v)) end)
  return r
end

local n = tonumber(io.read())
local x = {}
local y = {}
local h = {}
for i=1,n,1 do
  local arr = input()
  x[i] = arr[1]
  y[i] = arr[2]
  h[i] = arr[3]
end
local cx,cy
local H = 1e9+7
for i=0,100,1 do
  for j=0,100,1 do
    cx=i
    cy=j
    local flag = true
    for k=1,n,1 do
      local dx = math.abs(cx-x[k])
      local dy = math.abs(cy-y[k])
      if h[k]~=0 then
        local Hi = h[k]+dx+dy
        H = Hi
      end
    end
    for k=1,n,1 do
      local dx = math.abs(cx-x[k])
      local dy = math.abs(cy-y[k])
      local Hi = h[k]+dx+dy
      if h[k]==0 then
        if H>Hi then
          flag = false
        end
      else
        if H~=Hi then
          flag = false
        end
      end
    end
    if flag then
      local res = tostring(cx).." "..tostring(cy).." "..tostring(H)
      print(res)
    end
  end
end