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"
	"log"
	"math/rand"
	"os"
	"strconv"
	"time"
)

func main() {
	log.SetFlags(log.Lshortfile)
	rand.Seed(time.Now().UnixNano())
	N := nextInt()
	x := make([]int, N)
	y := make([]int, N)
	h := make([]int, N)
	idx := 0
	for i := 0; i < N; i++ {
		x[i] = nextInt()
		y[i] = nextInt()
		h[i] = nextInt()
		if h[i] != 0 {
			idx = i
		}
	}
	idx = rand.Intn(N)
	for cx := 0; cx <= 100; cx++ {
		for cy := 0; cy <= 100; cy++ {
			check := true
			hypothesis := abs(x[idx]-cx) + abs(y[idx]-cy) + h[idx]
			for i := 0; i < N; i++ {
				if h[i] == 0 {
					continue
				}
				h := abs(x[i]-cx) + abs(y[i]-cy) + h[i]
				if hypothesis != h {
					check = false
					break
				}
			}
			if check {
				trueHigh := abs(cx-x[idx]) + abs(cy-y[idx]) + h[idx]
				for i := 0; i < N; i++ {
					if h[i] == 0 {
						continue
					}
					if h[i] != max(trueHigh-abs(x[i]-cx)-abs(y[i]-cy), 0) {
						// log.Println(cx, cy, "gotoNEXT")
						goto NEXT
					}
				}
				fmt.Println(cx, cy, trueHigh)
				return
			}
		NEXT:
		}
	}
	z := nextInt()
	log.Println(z)
}
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}
func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}
func sum(a []int) (r int) {
	for i := range a {
		r += a[i]
	}
	return r
}
func minmax(a, b int) (int, int) {
	if a > b {
		return b, a
	}
	return a, b
}
func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

type Pair struct {
	a, b int
}

type Pairs []Pair

func (p Pairs) Len() int {
	return len(p)
}
func (p Pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

func (p Pairs) Less(i, j int) bool {
	return p[i].b < p[j].b
}

var nextReader func() string

func init() {
	nextReader = NewScanner()
}

func NewScanner() func() string {
	r := bufio.NewScanner(os.Stdin)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)
	return func() string {
		r.Scan()
		return r.Text()
	}
}
func nextString() string {
	return nextReader()
}
func nextInt64() int64 {
	v, _ := strconv.ParseInt(nextReader(), 10, 64)
	return v
}
func nextInt() int {
	v, _ := strconv.Atoi(nextReader())
	return v
}
func nextInts(n int) []int {
	r := make([]int, n)
	for i := 0; i < n; i++ {
		r[i] = nextInt()
	}
	return r
}
func nextFloat64() float64 {
	f, _ := strconv.ParseFloat(nextReader(), 64)
	return f
}