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.

Examples

Input

4
2 3 5
2 1 5
1 2 5
3 2 5


Output

2 2 6


Input

2
0 0 100
1 1 98


Output

0 0 100


Input

3
99 1 191
100 1 192
99 0 192


Output

100 0 193
#include <bits/stdc++.h>
using namespace std;

int main()
{
	int N;
	int X[105], Y[105], H[105];
	
	int idx = -1;
	cin >> N;
	for ( int i = 0; i < N; i++ ) {
		cin >> X[i] >> Y[i] >> H[i];
		if ( H[i] > 0 ) {
			idx = i;
		}
	}

	for ( int y = 0; y <= 100; y++ ) {
		for ( int x = 0; x <= 100; x++ ) {
			int pdist = abs(y - Y[idx]) + abs(x - X[idx]);
			int ph = H[idx] + pdist;
			bool flag = true;	
			for ( int i = 0; i < N; i++ ) {
				if ( max(0, ph - abs(y - Y[i]) - abs(x - X[i])) != H[i] ) {
					flag = false;
					break;
				}
			}
			if ( flag ) {
				cout << x << " " << y << " " << ph << endl;
				return ( 0 );
			}
		}
	}
}
