use std::collections::VecDeque;

use crate::atcoder8_library::binary_search::BinarySearchWithI64;

fn main() {
    let n = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse::<usize>().unwrap()
    };
    let mut xyt = Vec::new();
    for _ in 0..n {
        xyt.push({
            let mut line = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                iter.next().unwrap().parse::<i64>().unwrap(),
                iter.next().unwrap().parse::<i64>().unwrap(),
                iter.next().unwrap().parse::<usize>().unwrap(),
            )
        });
    }

    let mut ceil_sq_dist_mat = vec![vec![0; n]; n];

    for i in 0..n {
        let (x1, y1, t1) = xyt[i];
        let sq_r1 = x1.pow(2) + y1.pow(2);

        for j in (i + 1)..n {
            let (x2, y2, t2) = xyt[j];

            if t1 == t2 {
                let sq_dist = calc_sq_euclid_dist((x1, y1), (x2, y2));
                ceil_sq_dist_mat[i][j] = sq_dist;
                ceil_sq_dist_mat[j][i] = sq_dist;
            } else {
                // (r1 - r2)**2 = r1**2 - 2*r1*r2 + r2**2 = sq_r1 + sq_r2 - sqrt(4*sq_r1*sq_r2)
                let sq_r2 = x2.pow(2) + y2.pow(2);
                let ceil_sqrt = calc_floor_sqrt(4 * sq_r1 * sq_r2);
                let ceil_sq_dist = sq_r1 + sq_r2 - ceil_sqrt;
                ceil_sq_dist_mat[i][j] = ceil_sq_dist;
                ceil_sq_dist_mat[j][i] = ceil_sq_dist;
            }
        }
    }

    let is_ok = |s: i64| {
        let mut graph = vec![vec![]; n];

        for i in 0..n {
            for j in (i + 1)..n {
                if s >= ceil_sq_dist_mat[i][j] {
                    graph[i].push(j);
                    graph[j].push(i);
                }
            }
        }

        let mut que = VecDeque::from(vec![0]);
        let mut visited = vec![false; n];
        visited[0] = true;

        while let Some(cur) = que.pop_front() {
            for &next in &graph[cur] {
                if visited[next] {
                    continue;
                }

                visited[next] = true;
                que.push_back(next);
            }
        }

        visited[n - 1]
    };

    let ans = (0_i64..=3_200_000_000).binary_search(is_ok, false).unwrap();
    println!("{}", ans);
}

fn calc_sq_euclid_dist(coord1: (i64, i64), coord2: (i64, i64)) -> i64 {
    (coord1.0 - coord2.0).pow(2) + (coord1.1 - coord2.1).pow(2)
}

fn calc_floor_sqrt(n: i64) -> i64 {
    assert!(n >= 0);

    (0..=n).binary_search(|x| x.pow(2) <= n, true).unwrap()
}

pub mod atcoder8_library {
    pub mod binary_search {
        //! Implements binary search for range represented by the Rust's built-in range type.

        use std::ops::{
            Range, RangeBounds, RangeFrom, RangeFull, RangeInclusive, RangeTo, RangeToInclusive,
        };

        macro_rules! impl_binary_search_with_integer {
            ($int_type: ident, $fn_name_for_inc: ident, $fn_name_for_dec: ident, $fn_name: ident, $trait_name: ident) => {
                fn $fn_name_for_inc<R, F>(rng: R, mut is_ok: F) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => {
                            if start == std::$int_type::MAX {
                                return None;
                            }

                            start + 1
                        }
                        std::ops::Bound::Unbounded => std::$int_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => {
                            if end == std::$int_type::MAX {
                                if !is_ok(end) {
                                    return None;
                                }

                                end
                            } else {
                                end + 1
                            }
                        }
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$int_type::MAX,
                    };

                    if left >= right {
                        return None;
                    }

                    if is_ok(left) {
                        return Some(left);
                    }

                    if left + 1 == right || !is_ok(right - 1) {
                        return None;
                    }

                    while right - left > 1 {
                        let mid = left + (right - left) / 2;

                        if is_ok(mid) {
                            right = mid;
                        } else {
                            left = mid;
                        }
                    }

                    Some(right)
                }

                fn $fn_name_for_dec<R, F>(rng: R, mut is_ok: F) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => {
                            if start == std::$int_type::MAX {
                                return None;
                            }

                            start + 1
                        }
                        std::ops::Bound::Unbounded => std::$int_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => {
                            if end == std::$int_type::MAX {
                                if is_ok(end) {
                                    return Some(end);
                                }

                                end
                            } else {
                                end + 1
                            }
                        }
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$int_type::MAX,
                    };

                    if left >= right {
                        return None;
                    }

                    if is_ok(right - 1) {
                        return Some(right - 1);
                    }

                    if left + 1 == right || !is_ok(left) {
                        return None;
                    }

                    while right - left > 1 {
                        let mid = left + (right - left) / 2;

                        if is_ok(mid) {
                            left = mid;
                        } else {
                            right = mid;
                        }
                    }

                    Some(left)
                }

                /// If `is_ok` is monotonically increasing, returns the smallest integer `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// If `is_ok` is monotonically decreasing, returns the largest integer `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// Returns `None` if no such integer exists in both of the above cases.
                ///
                /// # Arguments
                ///
                /// * `rng` - Domain of function `is_ok`.
                /// * `is_ok` - Monotonic function.
                /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                /// or a monotonically increasing function if false.
                ///
                /// # Examples
                ///
                /// ```
                /// use atcoder8_library::binary_search::binary_search_with_i64;
                ///
                /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                /// assert_eq!(binary_search_with_i64(0..100, is_ok, false), Some(20));
                ///
                /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                /// assert_eq!(binary_search_with_i64(0..10, is_ok, false), None);
                ///
                /// let is_ok = |x: i64| { x.pow(3) < -8000 };
                /// assert_eq!(binary_search_with_i64(-100..0, is_ok, true), Some(-21));
                /// ```
                pub fn $fn_name<R, F>(rng: R, is_ok: F, dec: bool) -> Option<$int_type>
                where
                    R: RangeBounds<$int_type>,
                    F: FnMut($int_type) -> bool,
                {
                    if dec {
                        $fn_name_for_dec(rng, is_ok)
                    } else {
                        $fn_name_for_inc(rng, is_ok)
                    }
                }

                pub trait $trait_name: Sized + RangeBounds<$int_type> {
                    /// Performs a binary search on the domain specified by the Rust's built-in range type.
                    ///
                    /// If `is_ok` is monotonically increasing, returns the smallest integer `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// If `is_ok` is monotonically decreasing, returns the largest integer `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// Returns `None` if no such integer exists in both of the above cases.
                    ///
                    /// # Arguments
                    ///
                    /// * `is_ok` - Monotonic function.
                    /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                    /// or a monotonically increasing function if false.
                    ///
                    /// # Examples
                    ///
                    /// ```
                    /// use atcoder8_library::binary_search::BinarySearchWithI64;
                    ///
                    /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                    /// assert_eq!((0..100).binary_search(is_ok, false), Some(20));
                    ///
                    /// let is_ok = |x: i64| { x.pow(2) >= 400 };
                    /// assert_eq!((0..10).binary_search(is_ok, false), None);
                    ///
                    /// let is_ok = |x: i64| { x.pow(3) < -8000 };
                    /// assert_eq!((-100..0).binary_search(is_ok, true), Some(-21));
                    /// ```
                    fn binary_search<F>(self, is_ok: F, dec: bool) -> Option<$int_type>
                    where
                        F: FnMut($int_type) -> bool,
                    {
                        $fn_name(self, is_ok, dec)
                    }
                }

                impl $trait_name for RangeFull {}

                impl $trait_name for RangeTo<$int_type> {}

                impl $trait_name for RangeToInclusive<$int_type> {}

                impl $trait_name for RangeFrom<$int_type> {}

                impl $trait_name for Range<$int_type> {}

                impl $trait_name for RangeInclusive<$int_type> {}
            };
        }

        impl_binary_search_with_integer!(
            i8,
            binary_search_with_i8_for_inc,
            binary_search_with_i8_for_dec,
            binary_search_with_i8,
            BinarySearchWithI8
        );

        impl_binary_search_with_integer!(
            i16,
            binary_search_with_i16_for_inc,
            binary_search_with_i16_for_dec,
            binary_search_with_i16,
            BinarySearchWithI16
        );

        impl_binary_search_with_integer!(
            i32,
            binary_search_with_i32_for_inc,
            binary_search_with_i32_for_dec,
            binary_search_with_i32,
            BinarySearchWithI32
        );

        impl_binary_search_with_integer!(
            i64,
            binary_search_with_i64_for_inc,
            binary_search_with_i64_for_dec,
            binary_search_with_i64,
            BinarySearchWithI64
        );

        impl_binary_search_with_integer!(
            i128,
            binary_search_with_i128_for_inc,
            binary_search_with_i128_for_dec,
            binary_search_with_i128,
            BinarySearchWithI128
        );

        impl_binary_search_with_integer!(
            isize,
            binary_search_with_isize_for_inc,
            binary_search_with_isize_for_dec,
            binary_search_with_isize,
            BinarySearchWithIsize
        );

        impl_binary_search_with_integer!(
            u8,
            binary_search_with_u8_for_inc,
            binary_search_with_u8_for_dec,
            binary_search_with_u8,
            BinarySearchWithU8
        );

        impl_binary_search_with_integer!(
            u16,
            binary_search_with_u16_for_inc,
            binary_search_with_u16_for_dec,
            binary_search_with_u16,
            BinarySearchWithU16
        );

        impl_binary_search_with_integer!(
            u32,
            binary_search_with_u32_for_inc,
            binary_search_with_u32_for_dec,
            binary_search_with_u32,
            BinarySearchWithU32
        );

        impl_binary_search_with_integer!(
            u64,
            binary_search_with_u64_for_inc,
            binary_search_with_u64_for_dec,
            binary_search_with_u64,
            BinarySearchWithU64
        );

        impl_binary_search_with_integer!(
            u128,
            binary_search_with_u128_for_inc,
            binary_search_with_u128_for_dec,
            binary_search_with_u128,
            BinarySearchWithU128
        );

        impl_binary_search_with_integer!(
            usize,
            binary_search_with_usize_for_inc,
            binary_search_with_usize_for_dec,
            binary_search_with_usize,
            BinarySearchWithUsize
        );

        macro_rules! impl_binary_search_with_float {
            ($float_type: ident, $fn_name_for_inc: ident, $fn_name_for_dec: ident, $fn_name: ident, $trait_name: ident) => {
                fn $fn_name_for_inc<R, F>(
                    rng: R,
                    mut is_ok: F,
                    eps: $float_type,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => start,
                        std::ops::Bound::Unbounded => std::$float_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => end,
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$float_type::MAX,
                    };

                    assert!(
                        eps > 0.0,
                        "Allowable margin of error must be a positive number."
                    );

                    if left >= right {
                        return None;
                    }

                    if is_ok(left) {
                        return Some(left);
                    }

                    if !is_ok(right) {
                        return None;
                    }

                    while right - left > eps {
                        let mid = right - (right - left) / 2.0;

                        if mid <= left || right <= mid {
                            return None;
                        }

                        if is_ok(mid) {
                            right = mid;
                        } else {
                            left = mid;
                        }
                    }

                    Some(right)
                }

                fn $fn_name_for_dec<R, F>(
                    rng: R,
                    mut is_ok: F,
                    eps: $float_type,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    let mut left = match rng.start_bound() {
                        std::ops::Bound::Included(&start) => start,
                        std::ops::Bound::Excluded(&start) => start,
                        std::ops::Bound::Unbounded => std::$float_type::MIN,
                    };

                    let mut right = match rng.end_bound() {
                        std::ops::Bound::Included(&end) => end,
                        std::ops::Bound::Excluded(&end) => end,
                        std::ops::Bound::Unbounded => std::$float_type::MAX,
                    };

                    assert!(
                        eps > 0.0,
                        "Allowable margin of error must be a positive number."
                    );

                    if left >= right {
                        return None;
                    }

                    if is_ok(right) {
                        return Some(right);
                    }

                    if !is_ok(left) {
                        return None;
                    }

                    while (right - left) > eps {
                        let mid = right - (right - left) / 2.0;

                        if mid <= left || right <= mid {
                            return None;
                        }

                        if is_ok(mid) {
                            left = mid;
                        } else {
                            right = mid;
                        }
                    }

                    Some(left)
                }

                /// If `is_ok` is monotonically increasing,
                /// returns the smallest floating point number `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// If `is_ok` is monotonically decreasing,
                /// returns the largest floating point number `x`
                /// that satisfies `is_ok(x) = true` as the value of `Some`.
                ///
                /// Returns `None` if no such floating point number exists in both of the above cases.
                /// This includes the case where the absolute error cannot be determined
                /// to be less than or equal to `eps`.
                ///
                /// # Arguments
                ///
                /// * `rng` - Domain of function `is_ok`.
                /// * `is_ok` - Monotonic function.
                /// * `eps` - The allowable absolute error. It must be a positive number.
                /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                /// or a monotonically increasing function if false.
                ///
                /// # Examples
                ///
                /// ```
                /// use atcoder8_library::binary_search::binary_search_with_f64;
                ///
                /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                /// let ans = binary_search_with_f64(0.0..100.0, is_ok, 1e-6, false).unwrap();
                /// assert!((ans - 20.0).abs() <= 1e-6);
                ///
                /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                /// assert_eq!(binary_search_with_f64(0.0..10.0, is_ok, 1e-6, false), None);
                ///
                /// let is_ok = |x: f64| { x.powi(3) <= -8000.0 };
                /// let ans = binary_search_with_f64(-100.0..0.0, is_ok, 1e-6, true).unwrap();
                /// assert!((ans - (-20.0)).abs() <= 1e-6);
                /// ```
                pub fn $fn_name<R, F>(
                    rng: R,
                    is_ok: F,
                    eps: $float_type,
                    dec: bool,
                ) -> Option<$float_type>
                where
                    R: RangeBounds<$float_type>,
                    F: FnMut($float_type) -> bool,
                {
                    if dec {
                        $fn_name_for_dec(rng, is_ok, eps)
                    } else {
                        $fn_name_for_inc(rng, is_ok, eps)
                    }
                }

                pub trait $trait_name: Sized + RangeBounds<$float_type> {
                    /// Performs a binary search on the domain specified by the Rust's built-in range type.
                    ///
                    /// If `is_ok` is monotonically increasing,
                    /// returns the smallest floating point number `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// If `is_ok` is monotonically decreasing,
                    /// returns the largest floating point number `x`
                    /// that satisfies `is_ok(x) = true` as the value of `Some`.
                    ///
                    /// Returns `None` if no such floating point number exists in both of the above cases.
                    /// This includes the case where the absolute error cannot be determined
                    /// to be less than or equal to `eps`.
                    ///
                    /// # Arguments
                    ///
                    /// * `is_ok` - Monotonic function.
                    /// * `eps` - The allowable absolute error. It must be a positive number.
                    /// * `dec` - Represents that `is_ok` is a monotonically decreasing function if true,
                    /// or a monotonically increasing function if false.
                    ///
                    /// # Examples
                    ///
                    /// ```
                    /// use atcoder8_library::binary_search::BinarySearchWithF64;
                    ///
                    /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                    /// let ans = (0.0..100.0).binary_search(is_ok, 1e-6, false).unwrap();
                    /// assert!((ans - 20.0).abs() <= 1e-6);
                    ///
                    /// let is_ok = |x: f64| { x.powi(2) >= 400.0 };
                    /// assert_eq!((0.0..10.0).binary_search(is_ok, 1e-6, false), None);
                    ///
                    /// let is_ok = |x: f64| { x.powi(3) <= -8000.0 };
                    /// let ans = (-100.0..0.0).binary_search(is_ok, 1e-6, true).unwrap();
                    /// assert!((ans - (-20.0)).abs() <= 1e-6);
                    /// ```
                    fn binary_search<F>(
                        self,
                        is_ok: F,
                        eps: $float_type,
                        dec: bool,
                    ) -> Option<$float_type>
                    where
                        F: FnMut($float_type) -> bool,
                    {
                        $fn_name(self, is_ok, eps, dec)
                    }
                }

                impl $trait_name for RangeFull {}

                impl $trait_name for RangeTo<$float_type> {}

                impl $trait_name for RangeToInclusive<$float_type> {}

                impl $trait_name for RangeFrom<$float_type> {}

                impl $trait_name for Range<$float_type> {}

                impl $trait_name for RangeInclusive<$float_type> {}
            };
        }

        impl_binary_search_with_float!(
            f32,
            binary_search_with_f32_for_inc,
            binary_search_with_f32_for_dec,
            binary_search_with_f32,
            BinarySearchWithF32
        );

        impl_binary_search_with_float!(
            f64,
            binary_search_with_f64_for_inc,
            binary_search_with_f64_for_dec,
            binary_search_with_f64,
            BinarySearchWithF64
        );
    }
}