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"
	"os"
	"strconv"
)

var sc *bufio.Scanner

func init() {
	sc = bufio.NewScanner(os.Stdin)
	buffsize := 1000000
	buff := make([]byte, buffsize)
	sc.Buffer(buff, buffsize)
	sc.Split(bufio.ScanWords)
}

func loadint() (result int) {
	sc.Scan()
	result, _ = strconv.Atoi(sc.Text())
	return
}

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

func check(N, x, y int, xs, ys, hs []int) int {
	result := -1
	for i := 0; i < N; i++ {
		if hs[i] > 0 {
			d := abs(x-xs[i]) + abs(y-ys[i])
			if result > 0 && result != d+hs[i] {
				return 0
			}
			result = d + hs[i]
		}
	}
	for i := 0; i < N; i++ {
		if hs[i] == 0 {
			d := abs(x-xs[i]) + abs(y-ys[i])
			if result > 0 && result <= d+hs[i] {
				return 0
			}
		}
	}
	return result
}

func main() {
	N := loadint()
	xs := make([]int, N)
	ys := make([]int, N)
	hs := make([]int, N)
	for i := 0; i < N; i++ {
		xs[i] = loadint()
		ys[i] = loadint()
		hs[i] = loadint()
	}
	cx, cy, ch := 0, 0, 0
LOOP:
	for x := 0; x <= 100; x++ {
		for y := 0; y <= 100; y++ {
			h := check(N, x, y, xs, ys, hs)
			if h > 0 {
				cx, cy, ch = x, y, h
				break LOOP
			}
		}
	}
	fmt.Println(cx, cy, ch)
}