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;

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")
}

fn main() {
    let n: u32 = read();
    let (xs, ys, hs) = {
        let mut xs: Vec<i32> = Vec::new();
        let mut ys: Vec<i32> = Vec::new();
        let mut hs: Vec<i32> = Vec::new();
        for _ in 0..n {
            let s = {
                let mut s = String::new();
                std::io::stdin().read_line(&mut s).unwrap();
                s.trim_right().to_owned()
            };
            let mut ws = s.split_whitespace(); // 空白区切りの単語に分解する
            xs.push(ws.next().unwrap().parse().unwrap());
            ys.push(ws.next().unwrap().parse().unwrap());
            hs.push(ws.next().unwrap().parse().unwrap());
        } (xs, ys, hs) };

    for i in 0..101 {
        let (tf, j) = innor(i, xs.clone(), ys.clone(), hs.clone());
        if tf {
            let hh = hs[0] + i32::abs(xs[0] - i) + i32::abs(ys[0] - j);
            println!("{} {} {}", i, j, hh);
            return;
        }
    }
}

fn innor(i: i32, xs: Vec<i32>, ys: Vec<i32>, hs: Vec<i32>) -> (bool, i32) {
    for j in 0..101 {
        if tester(xs.clone(), ys.clone(), hs.clone(), i, j) {
            return (true, j);
        }
    }
    return (false, 0);
}

fn tester(x: Vec<i32>, y: Vec<i32>, h: Vec<i32>, i: i32, j: i32) -> bool {
    if h[0] < 1 {
        return false;
    }
    let hh = h[0] + i32::abs(x[0] - i) + i32::abs(y[0] - j);
    for k in 1..x.len() {
        if h[0] < 1 {
            return false;
        }
        if hh != h[k] + i32::abs(x[k] - i) + i32::abs(y[k] - j) {
            return false;
        }
    }
    return true;
}