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>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
using P = pair<ll, ll>;
#define rep(i, n) for(ll i=0;i<(ll)(n);i++)
#define rep1(i, n) for(ll i=1;i<=(ll)(n);i++)
#define rep2(i, m, n) for(ll i=m;i<(ll)(n);i++)
#define rrep(i, n, m) for(ll i=n;i>=(ll)(m);i--)
#define ALL(obj) (obj).begin(), (obj).end()
#define MOD 1000000007
#define INF 100000000000

ll d[101][101][101];
ll k[101][101][101];
ll cnt[101][101];

int main(void)
{
	cin.tie(0);
	ios::sync_with_stdio(false);

	ll N;

	cin >> N;

	vector<ll> x(N), y(N), h(N);
	rep(i, N) {
		cin >> x[i] >> y[i] >> h[i];
	}

	ll cx, cy, H;
	ll prev = 0;
	rep(i, 101) {
		rep(j, 101) {
			cnt[i][j] = true;
			rep(n, N) {
				d[n][i][j] = abs(x[n] - i) + abs(y[n] - j);
				if (h[n] != 0) {
					k[n][i][j] = h[n] + d[n][i][j];
					if (n != 0 && prev != k[n][i][j]) {
						cnt[i][j] = false;
						break;
					}
					prev = k[n][i][j];
				}
			}
		}
	}

	rep(i, 101) {
		rep(j, 101) {
			if (cnt[i][j]) {
				rep(n, N) {
					if (h[n] != max(k[n][i][j] - d[n][i][j], 0LL)) {
						cnt[i][j] = false;
					}
				}
			}
		}
	}

	rep(i, 101) {
		rep(j, 101) {
			if (cnt[i][j]) {
				cout << i << " " << j << " " << k[0][i][j] << "\n";
				break;
			}
		}
	}
	
	return 0;
}