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_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{VecDeque, HashSet, BTreeSet, BinaryHeap, HashMap};
#[allow(unused_imports)]
use std::io::{stdin, stdout, Write, BufReader, BufWriter};
#[allow(unused_imports)]
use std::io::prelude::BufRead;


fn main() {
    let mut heights = vec![vec![std::i64::MAX; 101]; 101];
    let n = read::<usize>();
    for _ in 0..n {
        let vec = read_vector::<i64>();
        let (x, y, h) = (vec[0], vec[1], vec[2]);
        for i in 0..101 {
            for j in 0..101 {
                if heights[i][j] == -1 {
                    continue;
                }
                let height = h + (i as i64 - x).abs() + (j as i64 - y).abs();
                if heights[i][j] == std::i64::MAX {
                    heights[i][j] = height;
                } else if heights[i][j] != height {
                    heights[i][j] = -1;
                }
            }
        }
    }

    for i in 0..101 {
        for j in 0..101 {
            if heights[i][j] != -1 {
                println!("{} {} {}", i, j, heights[i][j]);
                return;
            }
        }
    }
}

#[allow(dead_code)]
fn read<T>() -> T where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf
        .trim()
        .parse()
        .unwrap();
}

#[allow(dead_code)]
fn read_vector<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    let mut buf = String::with_capacity(100);
    stdin().read_line(&mut buf).unwrap();
    return buf
        .split_whitespace()
        .map(|s| s.parse().unwrap())
        .collect();
}

#[allow(dead_code)]
fn read_matrix<T>() -> Vec<Vec<T>> where T: std::str::FromStr, T::Err: std::fmt::Debug {
    use std::io::prelude::*;
    let stdin = stdin();
    let mut reader = BufReader::with_capacity(100 * 1024, stdin);
    let mut line = String::with_capacity(100);
    let mut matrix: Vec<Vec<T>> = Vec::new();

    while reader.read_line(&mut line).unwrap() > 0 {
        matrix.push(line
            .trim()
            .split_whitespace()
            .map(|s| s.parse().unwrap())
            .collect());
        line.clear();
    }

    return matrix;
}