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::stdin;
use std::iter::Iterator;
use std::collections::VecDeque;

fn main() {
    let mut cin = ConsoleInputWrapper::new();
    let N: usize = cin.input().parse().unwrap();
    let mut constraint = vec![(0, 0, 0); N];
    for i in 0..N {
        let x: i32 = cin.input().parse().unwrap();
        let y: i32 = cin.input().parse().unwrap();
        let h: i32 = cin.input().parse().unwrap();
        constraint[i] = (x, y, h);
    }

    for x in 0..101 {
        for y in 0..101 {
            let &(xx, yy, hh) = &constraint[0];
            let h = hh + (x - xx).abs() + (y - yy).abs();
            let mut flg = true;
            for &(xx, yy, hh) in &constraint {
                if h - (xx - x).abs() - (yy - y).abs() != hh {
                    flg = false;
                    break;
                }
            }
            if flg {
                println!("{} {} {}", x, y, h);
                return;
            }
        }
    }
//    let h = if (height[1][0] + height[0][1]) % 2 == 0 {
//        (height[1][0] + height[0][1] + 200) / 2
//    } else {
//        (height[0][0] + height[1][1] + 200) / 2
//    };
//    let y = if (height[0][0] + height[1][0]) % 2 == 0 {
//        h - (height[0][0] + height[1][0] + 100) / 2
//    } else {
//        -h + (height[0][1] + height[1][1] + 300) / 2
//    };
//    let x = if (height[0][0] + height[0][1]) % 2 == 0 {
//        h - (height[0][0] + height[0][1] + 100) / 2
//    } else {
//        -h + (height[1][0] + height[1][1] + 300) / 2
//    };
//    println!("{:?}", height);
//    println!("{} {} {}", max_height.0, max_height.1, max_height.2);
}

fn max(a: i32, b: i32) -> i32 {
    if b < a { a } else { b }
}

struct ConsoleInputWrapper {
    queue: VecDeque<String>
}

impl ConsoleInputWrapper {
    fn new() -> ConsoleInputWrapper {
        ConsoleInputWrapper {
            queue: VecDeque::new()
        }
    }
    fn input(&mut self) -> String {
        if self.queue.len() <= 0 {
            let mut s = String::new();
            stdin().read_line(&mut s).unwrap();
            let list: Vec<&str> = s.split_whitespace().collect();
            for string in list {
                self.queue.push_back(String::from(string));
            }
        }
        self.queue.pop_front().unwrap()
    }
}