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: Accepted)

#[allow(unused_imports)]
use template::buf_scan::*;
#[allow(unused_imports)]
use template::*;

#[allow(dead_code)]
#[macro_use]
pub mod macros {
    #[macro_export]
    macro_rules! debug {
        ($($a:expr),*) => {{
            use ::std::io::Write;
            writeln!(&mut ::std::io::stderr(), concat!($(stringify!($a), " = {:?}, "),*), $($a),*).unwrap();
        }}
    }

    #[macro_export]
    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut scanner = $crate::template::buf_scan::BufScanner::new($s.as_bytes());
            input_inner!{scanner, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = ::std::io::stdin();
            let mut scanner = $crate::template::buf_scan::BufScanner::new(stdin.lock());
            input_inner!{scanner, $($r)*}
        };
    }

    macro_rules! input_inner {
        ($scanner:expr) => {};
        ($scanner:expr, ) => {};
        ($scanner:ident, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($scanner, $t);
            input_inner!{$scanner $($r)*}
        };
        ($scanner:ident, mut $var:ident : $t:tt $($r:tt)*) => {
            let mut $var = read_value!($scanner, $t);
            input_inner!{$scanner $($r)*}
        };
    }

    macro_rules! read_value {
        ($scanner:ident, ( $($t:tt),* )) => {
            ( $(read_value!($scanner, $t)),* )
        };
        ($scanner:ident, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($scanner, $t)).collect::<Vec<_>>()
        };
        ($scanner:ident, chars) => {
            read_value!($scanner, String).chars().collect::<Vec<char>>()
        };
        ($scanner:ident, usize1) => {
            read_value!($scanner, usize) - 1usize
        };
        ($scanner:ident, $t:ty) => {
            ($scanner).next::<$t>()
        };
    }
}

fn main() {
    input! {
        n: usize,
        ps: [(i32, i32, i32); n],
    }
    for cx in 0..110 {
        for cy in 0..110 {
            let mut min_h = -1<<30;
            let mut max_h = 1<<30;
            for &(x, y, h) in ps.as_slice() {
                // h = max(H−|X−CX|−|Y−CY|,0)
                if h == 0 {
                    // H <= |X-CX| + |Y-CY|
                    max_h = std::cmp::min(max_h, (x-cx).abs() + (y-cy).abs());
                } else {
                    let ch = h + (x-cx).abs() + (y-cy).abs();
                    min_h = std::cmp::max(min_h, ch);
                    max_h = std::cmp::min(max_h, ch);
                }
            }
            if min_h <= max_h {
                println!("{} {} {}", cx, cy, min_h);
                return;
            }
        }
    }
}

#[allow(dead_code)]
pub mod template {
    pub mod buf_scan {
        pub struct BufScanner<R: ::std::io::BufRead> {
            br: R,
            buf: Vec<u8>,
            pos: usize,
        }

        impl<R: ::std::io::BufRead> BufScanner<R> {
            pub fn new(br: R) -> Self {
                BufScanner {
                    br: br,
                    buf: Vec::new(),
                    pos: 0usize,
                }
            }
            fn fill_line(&mut self) {
                self.buf.clear();
                self.pos = 0;
                self.br
                    .read_until(b'\n', &mut self.buf)
                    .expect("Read a line");
                if let Some(&b'\n') = self.buf.last() {
                    self.buf.pop();
                    if let Some(&b'\r') = self.buf.last() {
                        self.buf.pop();
                    }
                }
            }
            fn skip_space(&mut self) {
                loop {
                    for i in self.pos..self.buf.len() {
                        if self.buf[i] != b' ' {
                            self.pos = i;
                            return;
                        }
                    }
                    self.fill_line();
                }
            }
            pub fn read_token(&mut self) -> &str {
                self.skip_space();
                let start = self.pos;
                while self.pos < self.buf.len() && self.buf[self.pos] != b' ' {
                    self.pos += 1;
                }
                let ret = unsafe { ::std::str::from_utf8_unchecked(&self.buf[start..self.pos]) };
                self.pos += 1; // skip the last space (or len() + 1 which is fine)
                return ret;
            }
            pub fn next<T: ::std::str::FromStr>(&mut self) -> T {
                self.read_token().parse::<T>().ok().expect("Parse")
            }
        }
    }
}