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 fi first
#define se second
#define be begin
#define en end
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define ALL(a) (a).be() , (a).en()
#define REP(i,n) for(LL (i)=0;(i)<(n);(i)++)        //repeat n times
#define REP2(i,s,n) for(LL (i)=(s);(i)<(n);(i)++)   //repeat from s to n 
#define REPD(i,n) for(int (i)=(n);(i)>=0;(i)--)      //repeat from n to 0
#define REPD2(i,s,e) for(int (i)=(s);(i)>=(e);(i)--) //repeat from s to e
#define RANGE(i,v) for(auto &(i):v)                  //repeat range
#define ASIZE(a) (sizeof(a) / sizeof(a[0]))          //array size

using LL = long long;

template<typename T> using V = vector< T >;
using Vi = V<int>;
using Vll = V<LL>;
using Vs = V<string>;

template<typename T1,typename T2> using M = map< T1, T2>;
using Mii = M<int, int>;
using Msi = M<string, int>;

const int MOD = 1000000007;

int main(){
    LL N;
    cin>>N;
    Vll x(N),y(N),h(N);
    REP(i,N){
        cin>>x[i]>>y[i]>>h[i];
    }
    
    REP(cx,101){
        REP(cy,101){
            bool ok = true;
            LL H = 0;
            REP(i,N){
                if(h[i] == 0) continue;
                H = h[i]+abs(x[i]-cx)+abs(y[i]-cy);
            }
            REP(i,N){
                LL hi = max(H - abs(x[i]-cx) - abs(y[i]-cy), 0LL);
                if(h[i] != hi) ok = false;
            }
            if(ok) cout<<cx<<" "<<cy<<" "<<H<<endl;
        }
    }

    return 0;
}