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)

#[allow(unused)]
use std::io::*;
#[allow(unused)]
use std::str::*;
#[allow(unused)]
use std::collections::*;

pub fn read_from<T: FromStr, R: Read>(s: &mut R) -> T {
    let s = s.bytes().map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    if s.is_empty() {
        if cfg!(local) {
            // eprintln!("reached to EOF");
        }
        std::process::exit(0)
    }
    s.parse::<T>().unwrap_or_else(|_| panic!("faild to parse {}", s))
}

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let mut stdin = stdin.lock();
    read_from(&mut stdin)
}

pub const MOD: u64 = 1000000007;

fn check(cx: i64, cy: i64, xyh: &Vec<(i64, i64, i64)>) -> Option<i64> {
    let mut res = None;
    for &(x, y, h) in xyh.iter() {
        let dist = (x - cx).abs() + (y - cy).abs();
        if h > 0 {
            if let Some(ans) = res {
                if h + dist != ans {
                    return None
                }
            } else {
                res = Some(h + dist);
            }
        }
    }
    res
}

fn main() {
    loop {
        let n = read();
        let xyh: Vec<(i64, i64, i64)> = (0..n).map(|_| (read(), read(), read())).collect();
        let mut cand = Vec::new();
        for cx in 0..101 {
            for cy in 0..101 {
                if let Some(h) = check(cx, cy, &xyh) {
                    cand.push((cx, cy, h));
                }
            }
        }
        let p = if 1 < cand.len() { 1 } else { cand.len() - 1 };
        let (ax, ay, ah) = cand[p];
        println!("{} {} {}", ax, ay, ah);
    }
}