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>

int N;
int x[100],y[100],h[100];

int check(int a,int b);

int ab(int x){
	if(x<0)return -x;
	return x;
}

int min(int x,int y){
	if(x<y)return x;
	return y;
}

int main(){
	scanf("%d",&N);
	
	int H;
	for(int i=0;i<N;i++)scanf("%d%d%d",&x[i],&y[i],&h[i]);
	for(int i=0;i<=101;i++){
		for(int j=0;j<=101;j++){
			if(check(i,j)>0){
				H=check(i,j);
				printf("%d %d %d\n",i,j,H);
				return 0;
			}
		}
	}	
}

int check(int a,int b){
	int H=1000100000;
	int bound=1000010000;
	for(int i=0;i<N;i++){
		int dist=ab(a-x[i])+ab(b-y[i]);
		if(h[i]==0){
			bound=min(bound,dist);
		} else {
			if(H<1000000001 && H!=dist+h[i])return 0;
			H=dist+h[i];
		}
		if(H<1000000001 && H>bound)return 0;
	}
	if(H>bound)H=bound;
	return H;	
}