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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>
int main()
{
  long n;
  long x[101], y[101], h[101];
  long cx, cy, ch;
  long i,j,k,l;
  long minX=100, minY=100;
  long maxX=0, maxY=0;
  long maxH = 0;
  long hh[101], count;
  hh[0] = 0;

  scanf("%d",&n);
  for(k=1;k<=n;k++){
    scanf("%d %d %ld",&x[k],&y[k],&h[k]);
    /*
    if(minX>x[k])minX=x[k];
    if(minY>y[k])minY=y[k];
    if(maxX<x[k])maxX=x[k];
    if(maxY<y[k])maxY=y[k];
    */
  }
  l = 0;
  for(i=0;i<=100;i++){
    for(j=0;j<=100;j++){
      count = 0;
      for(k=1;k<=n;k++){
        hh[k] = abs(x[k]-i) + abs(y[k]-j) + h[k];
        if(hh[k]-hh[k-1]==0){
          count++;
        }
      }
      if(count==n-1){
        if(maxH<hh[1]){
          maxH=hh[1];
          cx = i;
          cy = j;
        }
      }
    }
  }
  printf("%d %d %d",cx,cy,maxH);
  return 0;
}