/*------------------------------------------------------------------*/
/*------------------------- begin template -------------------------*/
/*------------------------------------------------------------------*/

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

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

macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

use std::io;
use std::io::BufRead;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    pub reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
    pub fn fast_i64(&mut self) -> i64 {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            if begin == self.buf.len() {
                self.update_buf();
                continue;
            }
            let mut res = 0;
            let (is_positive, mut end) = match self.buf[begin] {
                b'+' => (true, begin + 1),
                b'-' => (false, begin + 1),
                _ => (true, begin),
            };
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return if is_positive { res } else { -res };
            } else {
                self.update_buf();
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;

fn main() {
    input! {
        new_stdin_parser = parser,
    }
    let res = solve(&mut parser);
    print!("{}", res);
}

/*------------------------------------------------------------------*/
/*-------------------------- end template --------------------------*/
/*------------------------------------------------------------------*/

#[derive(Clone, Copy, Debug)]
pub struct Vec3 {
    x: f64,
    y: f64,
    z: f64,
}

impl Vec3 {
    pub fn new(x: f64, y: f64, z: f64) -> Vec3 {
        Vec3 { x, y, z }
    }
    pub fn dist(v: Vec3, u: Vec3) -> f64 {
        let dx = u.x - v.x;
        let dy = u.y - v.y;
        let dz = u.z - v.z;
        (dx * dx + dy * dy + dz * dz).sqrt()
    }
    pub fn to_unit(&self) -> Vec3 {
        let d = (self.x * self.x + self.y * self.y + self.z * self.z).sqrt();
        Vec3 {
            x: self.x / d,
            y: self.y / d,
            z: self.z / d,
        }
    }
}

use std::ops::*;
impl Add for Vec3 {
    type Output = Vec3;
    fn add(self, v: Vec3) -> Vec3 {
        Vec3 {
            x: self.x + v.x,
            y: self.y + v.y,
            z: self.z + v.z,
        }
    }
}

impl Mul<f64> for Vec3 {
    type Output = Vec3;
    fn mul(self, a: f64) -> Vec3 {
        Vec3 {
            x: self.x * a,
            y: self.y * a,
            z: self.z * a,
        }
    }
}

use std::fmt::Write;
fn solve<R: BufRead>(parser: &mut Parser<R>) -> String {
    let mut buf = String::new();
    loop {
        input! {
            parser = parser,
            n: usize,
        }
        if n == 0 {
            break;
        }
        input! {
            parser = parser,
            ps: [(i64,i64,i64); n],
        }
        let eps = 1e-10;
        let mut res = 0.0;
        // <1>
        'l1: for &(x1, y1, l1) in &ps {
            let v = Vec3::new(x1 as f64, y1 as f64, l1 as f64);
            for &(x2, y2, l2) in &ps {
                let u = Vec3::new(x2 as f64, y2 as f64, 0.0);
                if !(Vec3::dist(u, v) < l2 as f64 + eps) {
                    continue 'l1;
                }
            }
            if res < v.z {
                res = v.z;
            }
        }
        // <2>
        for &(x1, y1, l1) in &ps {
            'l2: for &(x2, y2, l2) in &ps {
                let d = (((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)) as f64).sqrt();
                let d1 = ((l1 * l1 - l2 * l2) as f64 + d * d) / (2.0 * d);
                let h = (l1 as f64 * l1 as f64 - d1 * d1).sqrt();
                let v = Vec3::new(x1 as f64, y1 as f64, h)
                    + Vec3::new((x2 - x1) as f64, (y2 - y1) as f64, 0.0).to_unit() * d1;
                // eprintln!("d={}, d1={}, h={}", d, d1, h);
                // eprintln!("v={:?}", v);
                for &(x4, y4, l4) in &ps {
                    let u = Vec3::new(x4 as f64, y4 as f64, 0.0);
                    if !(Vec3::dist(u, v) < l4 as f64 + eps) {
                        continue 'l2;
                    }
                }
                if res < v.z {
                    res = v.z;
                }
            }
        }
        // <3>
        for &(x1, y1, l1) in &ps {
            for &(x2, y2, l2) in &ps {
                'l1: for &(x3, y3, l3) in &ps {
                    let a = -2 * (x1 - x2);
                    let b = -2 * (y1 - y2);
                    let c = l1 * l1 - l2 * l2 - x1 * x1 + x2 * x2 - y1 * y1 + y2 * y2;
                    let d = -2 * (x1 - x3);
                    let e = -2 * (y1 - y3);
                    let f = l1 * l1 - l3 * l3 - x1 * x1 + x3 * x3 - y1 * y1 + y3 * y3;
                    let x = (c * e - b * f) as f64 / (a * e - b * d) as f64;
                    let y = (a * f - c * d) as f64 / (a * e - b * d) as f64;
                    let z = ((l1 * l1) as f64
                        - (x - x1 as f64) * (x - x1 as f64)
                        - (y - y1 as f64) * (y - y1 as f64))
                        .sqrt();
                    let v = Vec3::new(x, y, z);
                    //// eprintln!("a={}, b={}, c={}, d={}, e={}, f={}", a, b, c, d, e, f);
                    //// eprintln!("v = {:?}", v);
                    for &(x4, y4, l4) in &ps {
                        let u = Vec3::new(x4 as f64, y4 as f64, 0.0);
                        if !(Vec3::dist(u, v) < l4 as f64 + eps) {
                            continue 'l1;
                        }
                    }
                    if res < v.z {
                        res = v.z;
                    }
                }
            }
        }
        // eprintln!("res = {}", res);
        writeln!(buf, "{:.20}", res);
    }
    buf
}



Measured memory_bytes: 5056