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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::*;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::HashSet;
use std::cmp;
use std::f64::consts;

fn main() {
    let n: i32 = read();
    let vec: Vec<(i32,i32,i32)> = (0..n).map(|_| (read(),read(),read())).collect();

    let mut ans: String = "".to_string();

    'outer: for cx in 0..101 {
        'inner: for cy in 0..101 {
            let mut set: HashSet<i32> = HashSet::new();

            let mut t0 = 0;
            let mut t1 = 0;
            let mut t2 = 0;
            for t in vec.iter() {
                t0 = t.0.clone();
                t1 = t.1.clone();
                t2 = t.2.clone();
                let height: i32 = calculate_height(
                    t.0,
                    cx,
                    t.1,
                    cy,
                    t.2
                );

                if height < 1 {
                    break 'inner;
                } else {
                    set.insert(height);
                }
            }

            let v: Vec<i32> = set.into_iter().collect();
            let top_height: i32 = v[0];

            if v.len() == 1 {
                let mut c = 0;
                for &v in vec.iter() {
                    let ok: bool = height_is_ok(
                        top_height,
                        t0,
                        cx,
                        t1,
                        cy,
                        t2
                    );
                    if ok {
                        c+=1;
                    }
                }
                if c == vec.len() {
                    ans = format!("{} {} {}", cx, cy, top_height);
                    break 'outer;
                }
            }
        }
    }

    println!("{}", ans);
}

fn height_is_ok(
    h: i32,
    xi: i32,
    cx: i32,
    yi: i32,
    cy: i32,
    hi: i32
) -> bool {
    let height = cmp::max((h-(xi-cx).abs() - (yi-cy).abs()), 0);
    return height == hi;
}

fn calculate_height(
                xi: i32,
                cx: i32,
                yi: i32,
                cy: i32,
                hi: i32
) -> i32 {
    return (xi-cx).abs() + (yi-cy).abs() + hi;
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}