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;

#define ll long long
#define ld long double
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define PI 3.14159265358979323846
#define sz(x) ((int)(x).size())

const int INF = 1e9;
const int MOD = 1e9 + 7;
const ll LINF = 1e18;
int main()
{
    int n;
    cin >> n;
    vector<tuple<int, int, int>> vc;
    tuple<int, int, int> G;

    rep(i, n)
    {
        int x, y, h;
        cin >> x >> y >> h;
        vc.push_back(make_tuple(x, y, h));
        if (h > 0)
        {
            G = make_tuple(x, y, h);
        }
    }

    for (int cx = 0; cx < 101; cx++)
    {
        for (int cy = 0; cy < 101; cy++)
        {
            int H = get<2>(G) + abs(cx - get<0>(G)) + abs(cy - get<1>(G));
            bool ok = true;
            rep(i, n)
            {
                int h_temp = max(H - abs(cx - get<0>(vc[i])) - abs(cy - get<1>(vc[i])),0);
                if (h_temp != get<2>(vc[i]))
                {
                    ok = false;
                    break;
                }
            }
            if(ok)
            {
                cout << cx << ' '<< cy << ' '<< H << endl;
                return 0;
            }
        }
    }
}