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 <stdlib.h>
#include <math.h>
#include <stdbool.h>
#define PI 3.141592653589793238462643383279


void change(int *x, int *y){
	int z;
	z = *x;
	*x = *y;
	*y = z;
}
int compare_int(const void *a, const void *b){
	return *(int*)a - *(int*)b;
}
int gcd(int a, int b)
{
    int c;
    if (a < b) {
        a+=b; b=a-b; a-=b;
    }
    while (b != 0) {
        c = a % b;
        a = b;
        b = c;
    }
    return a;
}

int main(void){
	int n;
	int x[101], y[101], h[101];
	int cx, cy, H=-1;
	int flag;
	scanf("%d", &n );
	for(int i=0;i<n;i++)	scanf("%d %d %d", &x[i], &y[i], &h[i]);
	
	for(int i=0;i<=100;i++){
		for(int j=0;j<=100;j++){
			H=-1;
			flag = 1;
			for(int k=0;k<n;k++){
				if(h[k]==0)	continue;
				else{
					H = h[k] + abs(i-x[k]) + abs(j-y[k]);
					break;
				}
			}
			if(H==-1){
				while(1){}
			}
			for(int k=0;k<n;k++){
				if(H != h[k] + abs(i-x[k]) + abs(j-y[k])){
					flag=0;
					break;
				}
			}
			if(flag==1){
				printf("%d %d %d", i,j,H);
				return 0;
			}
			
		}
	}
					
	return 0;
}