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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <utility>
using namespace std;

typedef long long ll;
ll MOD = 1e9+7;

int n;
int x[100];
int y[100];
ll h[100];

bool fff(int cx,int cy,ll ch)
{
	for(int i=0;i<n;i++)
	{
		ll ih=max(ch-abs(cx-x[i])-abs(cy-y[i]),0LL);
		if(ih!=h[i])
			return false;
	}
	return true;
}

int main()
{
	int ans=0;
	cin>>n;
	for(int i=0;i<n;i++)
		cin>>x[i]>>y[i]>>h[i];
	
	//最大高さを調べる
	ll mh=0;
	for(int i=0;i<n;i++)
		mh=max(mh,h[i]);

	//それぞれの座標ごとにmh+200まで調べる
	for(int i=0;i<101;i++)
	{
		for(int j=0;j<101;j++)
		{
			for(ll k=0;k<201;k++)
			{
				if(fff(i,j,k+mh))
				{
					cout<<i<<" "<<j<<" "<<k+mh<<endl;
					return 0;
				}
			}
		}
	}
	return 0;
}