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: Wrong Answer)

#include <iostream>
#include <iostream>
#include <stdio.h>
#include <cstring>
#include <math.h>
#include <algorithm>
#include <vector>
#include <string>
#include <stdlib.h>
#include <queue>
#include <stack>
#include <utility>
#include <fstream>
#include <random>
#include <map>
#include <unordered_map>
#include <cstdlib>
#define rep(i,n) for(int i=0;i<n;i++)
#define rrep(i,n) for(int i=n-1;i>=0;i--)
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define ll long long
#define INF 1000000001
#define mod 1000000007
#define p pair<int,int>
#define reverse(s) reverse(s.begin(), s.end());
int dx[4] = { 0,1,0,-1 };
int dy[4] = { 1,0,-1,0 };
using namespace std;
int POW(int x, int y) { return int(pow(double(x), double(y))); }



int main() {
	int n;
	cin >> n;
	vector<int>x(n), y(n), h(n);
	rep(i, n) {
		cin >> x[i] >> y[i] >> h[i];
	}
	rep(i,101){
		rep(j, 101) {
			bool flg = 1;
			int ansh = 0;
			vector<int> ika;
			rep(k, n) {
				if (h[k] > 0) {
					int h0 = h[k] + abs(i - x[k]) + abs(j - y[k]);
					if (h0 > 0) {
						if (ansh == 0) {
							ansh = h0;
						}
						else {
							if (ansh != h0) {
								flg = 0;
							}
						}
					}
				}
				else {
					int h0 = h[k] + abs(i - x[k]) + abs(j - y[k]);
					ika.push_back(h0);
				}
			}
			if (ansh>0) {
				rep(i, ika.size()) {
					if (ansh < ika[i]) {
						flg = 0;
					}
				}
				if (flg == 1) {
					cout << i << " " << j << " " << ansh << endl;
					return 0;
				}
			}
		}
	}
	vector<int> cc(1);
	cc[1] = 0;
	return 0;
}