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: Wrong Answer)

#include <bits/stdc++.h>
#define pt(sth) cout << sth << "\n"
#define chmax(a, b) {if(a<b) a=b;}
#define chmin(a, b) {if(a>b) a=b;}
#define moC(a, s, b) (a)=((a)s(b)+MOD)%MOD
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
static const ll INF=1e18;
static const ll MAX=101010;
static const ll MOD=1e9+7;
static const ll LOGN=55;




int main(void) {
  ll N;
  cin >> N;
  ll x[111], y[111], h[111];
  ll i;
  
  for(i=0; i<N; i++) {
    cin >> x[i] >> y[i] >> h[i];
  }
  
  for(ll cx=0; cx<=100; cx++) {
    for(ll cy=0; cy<=100; cy++) {
      
      
      ll t=0;
      for(i=0; i<N; i++) {
        if(h[i]==0) continue;
        t=h[i]+abs(x[i]-cx)+abs(y[i]-cy);
      }
      
      ll f=1;
      for(i=0; i<N; i++) {
        if(h[i]==0) continue;
        ll tt=h[i]+abs(x[i]-cx)+abs(y[i]-cy);
        
        if(tt!=t) f=0;
      }
      
      if(f) {
        pt(cx<<" "<<cy<<" "<<t);
        return 0;
      }
      
      
    }
  }
  
  
  
}