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 <vector>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <random>
#include <chrono>
#include <queue>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
#define INF 1000000000
#define MOD 1000000007

int main(){
    int N; cin >> N;
    vector<vector<int>> T(N, vector<int>(3));

    for(vector<int> &t:T)
        cin >> t[0] >> t[1] >> t[2];

    map<int, int> M;
    vector<vector<int>> o;
    for(int i=0; i<=100; i++){
        for(int j=0; j<=100; j++){
            for(int k=0; k<N; k++){
                if(T[k][2]==0) continue;
                M[T[k][2]+abs(i-T[k][0])+abs(j-T[k][1])]++;
            }
            if(M.size()==1) o.push_back({i, j, M.begin()->first});
            M.clear();
        }
    }
    
    for(int i=0; i<o.size(); i++){
        bool f = true;
        for(int j=0; j<N; j++){
            if(T[j][2]==0 && max(0, o[i][2] - abs(o[i][0]-T[j][0]) - abs(o[i][1]-T[j][1]))!=0) f = false;
        }
        if(f) cout << o[i][0] << " " << o[i][1] << " " << o[i][2] << endl;
    }
    return 0;
}