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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  n,i,j:integer;
  x,y:array[1..100] of integer;
  h:array[1..100] of longint;
function abs(x:longint):longint;
begin
  if x<0 then
  begin
    abs:=-x;
  end
  else
  begin
    abs:=x;
  end;
end;
function check(xx,yy:integer):boolean;
var
  now:integer;
  tmpw:longint;
begin
  for now:=1 to n do
  begin
    if h[now]<>0 then
    begin
      tmpw:=h[now]+abs(x[now]-xx)+abs(y[now]-yy);
      break;
    end;
  end;
  check:=true;
  for now:=1 to n do
  begin
    if not ((tmpw-abs(x[now]-xx)-abs(y[now]-yy)=h[now]) or ((tmpw-abs(x[now]-xx)-abs(y[now]-yy)<0) and (h[now]=0))) then
    begin
      check:=false;
      break;
    end;
  end;
end;
function get(xx,yy:integer):longint;
var
  now:integer;
begin
  for now:=1 to n do
  begin
    if h[now]<>0 then
    begin
      get:=h[now]+abs(x[now]-xx)+abs(y[now]-yy);
      break;
    end;
  end;
end;
begin
  readln(n);
  for i:=1 to n do
  begin
    readln(x[i],y[i],h[i]);
  end;
  for i:=0 to 100 do
  begin
    for j:=0 to 100 do
    begin
      if check(i,j) then
      begin
        writeln(i,' ',j,' ',get(i,j));
        exit;
      end;
    end;
  end;
end.