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 <bits/stdc++.h>

using namespace std;

using ll = long long;

int main() {
    int N;
    cin >> N;
    std::vector<ll> x(N), y(N), h(N);

    ll xt = 0, yt = 0, ht = 0;
    for (int i = 0; i < N; ++i) {
        cin >> x[i] >> y[i] >> h[i];
        if (h[i] != 0) {
            xt = x[i];
            yt = y[i];
            ht = h[i];
        }
    }

    for (int cx = 0; cx <= 100; ++cx) {
        for (int cy = 0; cy <= 100; ++cy) {
            const auto height = ht + std::abs(cx - xt) + std::abs(cy - yt);
            bool is_ok = true;
            for (int i = 0; i < N; ++i) {
                if (h[i] != std::max(height - std::abs(cx - x[i]) - std::abs(cy - y[i]), 0ll)) {
                    is_ok = false;
                }
            }
            if (is_ok) {
                cout << cx << " " << cy << " " << height << endl;
                return 0;
            }
        }
    }

    return 0;
}