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: Accepted)

#include <stdio.h>

int absl(int a){
  if(a>0){
    return a;
  }
  return -a;
}

int main(){
  int N,i;
  scanf("%d",&N);
  int x[N];int y[N];int h[N];
  for(i=0;i<N;i++){
    scanf("%d%d%d",&x[i],&y[i],&h[i]);
  }
  int cx,cy,H;
  int j=0;
  int flag;
  
  for(cx=0;cx<=100;cx++){
      for(cy=0;cy<=101;cy++){
      flag=0;j=0;
      while(h[j]==0){j++;}
      H=h[j]+absl(x[j]-cx)+absl(y[j]-cy);

      if(1<=j){
        for(i=0;i<j;i++){
          if(H-absl(x[i]-cx)-absl(y[i]-cy)>0){
            flag=1;
            break;
          }
        }
      }
      if(flag==0&&j==N-1){
	printf("%d %d %d",cx,cy,H);
	return 0;
      }
     
      for(i=j+1;i<N;i++){
	if(h[i]==0){
	  if(H-absl(x[i]-cx)-absl(y[i]-cy)>0) {
	    flag=1;
	    break;
	  }
	}
	if(h[i]>0){
	  if(h[i] != H-absl(x[i]-cx)-absl(y[i]-cy)) {
	    flag=1;
	    break;
	  }
	}
      }
      if(flag==0){
	printf("%d %d %d",cx,cy,H);
	return 0;
      }
    }
  }
  return 0;
}