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 <functional>

using namespace std;
typedef long long ll;
const int MAXN = 110;

struct pos {
  ll x, y, h;
};

bool compare(const pos& lhs, const pos& rhs) {
  return lhs.h > rhs.h;
}

int n;
pos positions[MAXN];

bool check(int cx, int cy, int& h) {
  h = positions[0].h + abs(positions[0].x - cx) + abs(positions[0].y - cy);
  for (int i=1;i<n;i++) {
    if (positions[i].h != max<ll>(h - abs(positions[i].x - cx) - abs(positions[i].y - cy), 0)) {
      return false;
    }
  }
  return true;
}

void solve() {
  sort(positions, positions + n, compare);
  for (int x=0;x<=100;x++) {
    for (int y=0;y<=100;y++) {
      int h;
      if (check(x, y, h)) {
        cout << x << " " << y << " " << h << endl;
        return;
      }
    }
  }
}

int main() {
  cin >> n;
  for (int i=0;i<n;i++) {
    cin >> positions[i].x >> positions[i].y >> positions[i].h;
  }
  solve();
}