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 all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define rep(i, s, N) for(ll i{s}; i < N; i++)
#define rem(i, N, s) for(ll i{N}; i > s; i--)
using namespace std;using ll = long long int;using ld = long double;using P = pair<ll,ll>;const int MOD = (int)1e9+7;const string rt = "\n";const string sp = " ";/* 最大公約数 */template<typename T> T gcd(T a, T b){return b != 0 ? gcd(b, a % b) : a;}/* UnionFind */template<typename T> struct UnionFind{vector<T> par;UnionFind(T n) : par(n, -1){}void init(T n){par.assign(n, -1);}T root(T x){if (par[x] < 0) return x;else return par[x] = root(par[x]);}bool issame(T x, T y){return root(x) == root(y);}bool merge(T x, T y){x = root(x); y = root(y);if(x == y) return false;if(par[x] > par[y]) swap(x, y);par[x] += par[y];par[y] = x;return true;}int size(int x) {return -par[root(x)];}};/* コンビネーション */template<typename T> ll combpm(T N_, T C_) {const int NUM_=400001;static ll fact[NUM_+1],factr[NUM_+1],inv[NUM_+1];if (fact[0]==0) {inv[1]=fact[0]=factr[0]=1;for (int i=2;i<=NUM_;++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;for (int i=1;i<=NUM_;++i) fact[i]=fact[i-1]*i%MOD, factr[i]=factr[i-1]*inv[i]%MOD;}if(C_<0 || C_>N_) return 0;return factr[C_]*fact[N_]%MOD*factr[N_-C_]%MOD;}/* 多次元ベクター */template<class T>vector<T> mvec(size_t a){return vector<T>(a);}template<class T, class... Ts>auto mvec(size_t a, Ts... ts){return vector<decltype(mvec<T>(ts...))>(a, mvec<T>(ts...));}/* テスト関数 */void test(ll n){cout << "test" << n << endl;}/* 小数点以下 */void fixsp(ll n){cout << fixed << setprecision(n);}void defsp(ll n){cout << defaultfloat << setprecision(n);}/* 重み付きUnionFind */struct WUnionFind {vector<int> par;vector<int> rank;WUnionFind(int n = 1) {init(n);}void init(int n = 1) {par.resize(n); rank.resize(n);for (int i = 0; i < n; ++i) par[i] = i, rank[i] = 0;}int root(int x) {if (par[x] == x) {return x;}else {int r = root(par[x]);return par[x] = r;}}bool issame(int x, int y) {return root(x) == root(y);}bool merge(int x, int y) {x = root(x); y = root(y);if (x == y) return false;if (rank[x] < rank[y]) swap(x, y);if (rank[x] == rank[y]) ++rank[x];par[y] = x;return true;}};/* IO高速化 */void fastio(){ios::sync_with_stdio(false);cin.tie(NULL);}
/* ここからコード開始 */

int main(){
  fastio;
  ll N;
  cin >> N;
  auto xyh = mvec<ll>(0,3);
  ll hmin{MOD};
  rep(i,0,N){
    ll x, y, h;
    cin >> x >> y >> h;
    hmin = min(hmin, h);
    xyh.push_back({x, y, h});
  }
  rep(x, 0, 101) rep(y, 0, 101) rep(h, hmin, hmin+201){
    bool isanswer{true};
    for(auto&& i : xyh){
      if(abs(x-i[0])+abs(y-i[1])+i[2] != h) isanswer = false;
    }
    if(isanswer){
      cout << x << sp << y << sp << h << rt;
      return 0;
    }
  }
}