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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

type point struct {
	x int
	y int
	h int
}

func abs(n int) int {
	if n < 0 {
		return -n
	}
	return n
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func maxph(ps []point) int {
	ans := ps[0].h
	for _, p := range ps {
		if p.h > ans {
			ans = p.h
		}
	}
	return ans
}

func main() {
	var n int
	fmt.Scan(&n)
	ps := make([]point, n)
	for i := range ps {
		fmt.Scan(&ps[i].x, &ps[i].y, &ps[i].h)
	}

	for ch := maxph(ps); ; ch++ {
		for cx := 0; cx <= 100; cx++ {
		L:
			for cy := 0; cy <= 100; cy++ {
				for _, p := range ps {
					if p.h != max(ch-abs(p.x-cx)-abs(p.y-cy), 0) {
						continue L
					}
				}
				fmt.Println(cx, cy, ch)
				return
			}
		}
	}
}