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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.ParseInt(sc.Text(), 10, 64)
	if e != nil {
		panic(e)
	}
	return int(i)
}

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	n := nextInt()

	xl := make([]int, n, n)
	yl := make([]int, n, n)
	hl := make([]int, n, n)
	for i := 0; i < n; i++ {
		xl[i] = nextInt()
		yl[i] = nextInt()
		hl[i] = nextInt()
	}

	max := 100
	for x := 0; x <= max; x++ {
		for y := 0; y <= max; y++ {
			needH := -1
			for i := 0; i < n; i++ {
				if hl[i] != 0 {
					dist := hl[i] + int(math.Abs(float64(x-xl[i]))) + int(math.Abs(float64(y-yl[i])))
					if needH == -1 {
						needH = dist
					} else {
						if dist != needH {
							needH = -2
							break
						}
					}
				}

			}

			if needH == -2 {
				continue
			}

			for i := 0; i < n; i++ {
				if hl[i] == 0 {
					dist := int(math.Abs(float64(x-xl[i]))) + int(math.Abs(float64(y-yl[i])))
					if dist > needH {
						needH = -2
						break
					}
				}
			}

			if needH == -2 {
				continue
			}

			fmt.Printf("%v %v %v\n", x, y, needH)
			return
		}
	}
}