Problem:
Score : 800 points

Problem Statement

There are N cards placed on a grid with H rows and W columns of squares.

The i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.

Multiple cards may be placed on the same square.

You will first pick up at most one card from each row.

Then, you will pick up at most one card from each column.

Find the maximum possible sum of the integers written on the picked cards.

Constraints

All values are integers.

1 \leq N \leq 10^5

1 \leq H, W \leq 10^5

1 \leq A_i \leq 10^5

1 \leq R_i \leq H

1 \leq C_i \leq W

Input

Input is given from Standard Input in the following format:

N H W
R_1 C_1 A_1
R_2 C_2 A_2
\vdots
R_N C_N A_N

Output

Print the maximum possible sum of the integers written on the picked cards.

Sample Input 1

6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4

Sample Output 1

28

The sum of the integers written on the picked cards will be 28, the maximum value possible, if you pick up cards as follows:

Pick up the fourth card from the first row.

Pick up the sixth card from the second row.

Pick up the second card from the first column.

Pick up the fifth card from the second column.

Sample Input 2

13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537

Sample Output 2

430590

Sample Input 3

1 100000 100000
1 1 1

Sample Output 3

1

Solution in Rust (1.42.0) (judge verdict: Accepted)

// SNIPPET vec_union_find_sets
pub struct VecUnionFindSets {
    set_count: usize,  items: Vec<VecUnionFindNode>
}
#[derive(Clone)]
struct VecUnionFindNode {
    parent: std::cell::Cell<usize>,
    len: usize
}
impl VecUnionFindNode {
    fn new(item: usize) -> VecUnionFindNode {
        VecUnionFindNode {
            parent: std::cell::Cell::new(item),
            len: 1
        }
    }
}
impl VecUnionFindSets {
    pub fn new() -> VecUnionFindSets {
        VecUnionFindSets {
            set_count: 0,
            items: Vec::new()
        }
    }
    pub fn with_items(items_count: usize) -> VecUnionFindSets {
        let mut sets = VecUnionFindSets::new();
        sets.add_items(items_count);
        sets
    }
    fn error_msg(items: &[usize]) -> String {
        assert!(items.len() == 1 || items.len() == 2);
        if items.len() == 1 {
            format!("no set contains {}", items[0])
        } else {
            format!("no set contains {} and no set contains {}", items[0], items[1])
        }
    }
    pub fn add_items(&mut self, count: usize) {
        self.set_count += count;
        let new_items = (self.items_len()..self.items_len()+count)
            .map(|i| VecUnionFindNode::new(i));
        self.items.extend(new_items);
    }
    pub fn items_len(&self) -> usize {
        self.items.len()
    }
    fn find(&self, item: usize) -> Option<usize> {
        if item >= self.items_len() {
            return None;
        }
        fn go(sets: &VecUnionFindSets, item: usize) -> usize {
            let node = &sets.items[item];
            if node.parent.get() == item {
                return item;
            }
            let root = go(sets, node.parent.get());
            sets.items[root].parent.set(root);
            root
        }
        Some(go(self, item))
    }
    pub fn count(&self) -> usize {
        self.set_count
    }
    pub fn len_of(&self, item: usize) -> Result<usize, String> {
        self.find(item).map(|root| self.items[root].len).ok_or_else(|| {
            VecUnionFindSets::error_msg(&[item])
        })
    }
    pub fn set_eq(&self, item1: usize, item2: usize) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some(root1), Some(root2)) => Ok(root1 == root2),
            (Some(_), None) => Err(VecUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(VecUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(VecUnionFindSets::error_msg(&[item1, item2])),
        }
    }
    pub fn unite(&mut self, item1: usize, item2: usize) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some(root1), Some(root2)) => {
                if root1 == root2 {
                    return Ok(false);
                }
                self.set_count -= 1;
                let (new_root, new_child) = if self.items[root1].len < self.items[root2].len {
                    (root2, root1)
                } else {
                    (root1, root2)
                };
                let new_len = self.items[root1].len + self.items[root2].len;
                self.items[new_root] = VecUnionFindNode {
                    parent: std::cell::Cell::new(new_root),
                    len: new_len
                };
                self.items[new_child] = VecUnionFindNode {
                    parent: std::cell::Cell::new(new_root),
                    len: 0
                };
                Ok(true)
            },
            (Some(_), None) => Err(VecUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(VecUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(VecUnionFindSets::error_msg(&[item1, item2]))
        }
    }
    pub fn iter_cloned(&self) -> impl Iterator<Item=Vec<usize>> {
        let mut sets = vec![Vec::new(); self.items_len()];
        for i in 0..self.items_len() {
            let repr = self.find(i).unwrap();
            sets[repr].push(i);
        }
        sets.into_iter().filter(|v| !v.is_empty())
    }
}
impl std::fmt::Debug for VecUnionFindSets {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{{")?;
        let mut first = true;
        for set in self.iter_cloned() {
            if !first {
                write!(f, ", ")?;
            }
            write!(f, "{:?}", set)?;
            first = false;
        }
        write!(f, "}}")
    }
}
/*
impl<T: Eq + std::hash::Hash + std::fmt::Debug> IntoIterator for HashUnionFindSets<T> {
    type Item = HashSet<T>;
    type IntoIter = std::collections::hash_map::Values<>;
    fn into_iter(self) -> Self::IntoIter {
    }
}
*/

// SNIPPET read
pub trait Readable {
    type Output;
    const WORD_COUNT: usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            const WORD_COUNT: usize = $words_count;
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
pub struct Bytes();
impl Readable for Bytes {
    type Output = Vec<u8>;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Vec<u8>, String> {
        Ok(words[0].bytes().collect())
    }
}
impl Readable for i8 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i8, String> {
        use std::str::FromStr;
        i8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i8", words[0])
        })
    }
}
impl Readable for u8 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u8, String> {
        use std::str::FromStr;
        u8::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u8", words[0])
        })
    }
}
impl Readable for i16 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i16, String> {
        use std::str::FromStr;
        i16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i16", words[0])
        })
    }
}
impl Readable for u16 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u16, String> {
        use std::str::FromStr;
        u16::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u16", words[0])
        })
    }
}
impl Readable for i32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i32, String> {
        use std::str::FromStr;
        i32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i32", words[0])
        })
    }
}
impl Readable for u32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u32, String> {
        use std::str::FromStr;
        u32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u32", words[0])
        })
    }
}
impl Readable for i64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i64, String> {
        use std::str::FromStr;
        i64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u64, String> {
        use std::str::FromStr;
        u64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for i128 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<i128, String> {
        use std::str::FromStr;
        i128::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as i64", words[0])
        })
    }
}
impl Readable for u128 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<u128, String> {
        use std::str::FromStr;
        u128::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as u64", words[0])
        })
    }
}
impl Readable for isize {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<isize, String> {
        use std::str::FromStr;
        <isize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as isize", words[0])
        })
    }
}
impl Readable for usize {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<usize, String> {
        use std::str::FromStr;
        <usize>::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as usize", words[0])
        })
    }
}
impl Readable for f32 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<f32, String> {
        use std::str::FromStr;
        f32::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f32", words[0])
        })
    }
}
impl Readable for f64 {
    type Output = Self;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<f64, String> {
        use std::str::FromStr;
        f64::from_str(words[0]).map_err(|_| {
            format!("cannot parse `{}` as f64", words[0])
        })
    }
}
#[allow(non_camel_case_types)]
pub struct u8_;
impl Readable for u8_ {
    type Output = u8;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u8::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u16_;
impl Readable for u16_ {
    type Output = u16;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u16::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u32_;
impl Readable for u32_ {
    type Output = u32;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u32::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct u64_;
impl Readable for u64_ {
    type Output = u64;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        u64::read_words(words).map(|n| n-1)
    }
}
#[allow(non_camel_case_types)]
pub struct usize_;
impl Readable for usize_ {
    type Output = usize;
    const WORD_COUNT: usize = 1;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        <usize>::read_words(words).map(|n| n-1)
    }
}
impl<T1: Readable, T2: Readable> Readable for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let val2 = T2::read_words(&words[start..])?;
        Ok((val1, val2))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable> Readable for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let val3 = T3::read_words(&words[start..])?;
        Ok((val1, val2, val3))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable> Readable for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let val4 = T4::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable> Readable for (T1, T2, T3, T4, T5) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT + T5::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::WORD_COUNT;
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let val5 = T5::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5))
    }
}
impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, T5: Readable, T6: Readable> Readable for (T1, T2, T3, T4, T5, T6) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output, T5::Output, T6::Output);
    const WORD_COUNT: usize = T1::WORD_COUNT + T2::WORD_COUNT + T3::WORD_COUNT + T4::WORD_COUNT + T5::WORD_COUNT + T6::WORD_COUNT;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let mut start = 0;
        let count1 = T1::WORD_COUNT;
        let val1 = T1::read_words(&words[start .. start+count1])?;
        start += count1;
        let count2 = T2::WORD_COUNT;
        let val2 = T2::read_words(&words[start .. start+count2])?;
        start += count2;
        let count3 = T3::WORD_COUNT;
        let val3 = T3::read_words(&words[start .. start+count3])?;
        start += count3;
        let count4 = T4::WORD_COUNT;
        let val4 = T4::read_words(&words[start .. start+count4])?;
        start += count4;
        let count5 = T5::WORD_COUNT;
        let val5 = T5::read_words(&words[start .. start+count5])?;
        start += count5;
        let val6 = T6::read_words(&words[start..])?;
        Ok((val1, val2, val3, val4, val5, val6))
    }
}
impl<T: Readable> Readable for [T; 2] {
    type Output = [T::Output; 2];
    const WORD_COUNT: usize = T::WORD_COUNT * 2;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        Ok([val1, val2])
    }
}
impl<T: Readable> Readable for [T; 3] {
    type Output = [T::Output; 3];
    const WORD_COUNT: usize = T::WORD_COUNT * 3;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        Ok([val1, val2, val3])
    }
}
impl<T: Readable> Readable for [T; 4] {
    type Output = [T::Output; 4];
    const WORD_COUNT: usize = T::WORD_COUNT * 4;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        Ok([val1, val2, val3, val4])
    }
}
impl<T: Readable> Readable for [T; 5] {
    type Output = [T::Output; 5];
    const WORD_COUNT: usize = T::WORD_COUNT * 5;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        let val5 = T::read_words(&words[T::WORD_COUNT*4 .. T::WORD_COUNT*5])?;
        Ok([val1, val2, val3, val4, val5])
    }
}
impl<T: Readable> Readable for [T; 6] {
    type Output = [T::Output; 6];
    const WORD_COUNT: usize = T::WORD_COUNT * 6;
    fn read_words(words: &[&str]) -> Result<Self::Output, String> {
        assert_eq!(words.len(), Self::WORD_COUNT);
        let val1 = T::read_words(&words[T::WORD_COUNT*0 .. T::WORD_COUNT*1])?;
        let val2 = T::read_words(&words[T::WORD_COUNT*1 .. T::WORD_COUNT*2])?;
        let val3 = T::read_words(&words[T::WORD_COUNT*2 .. T::WORD_COUNT*3])?;
        let val4 = T::read_words(&words[T::WORD_COUNT*3 .. T::WORD_COUNT*4])?;
        let val5 = T::read_words(&words[T::WORD_COUNT*4 .. T::WORD_COUNT*5])?;
        let val6 = T::read_words(&words[T::WORD_COUNT*5 .. T::WORD_COUNT*6])?;
        Ok([val1, val2, val3, val4, val5, val6])
    }
}
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    line.trim_end_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::WORD_COUNT {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::WORD_COUNT));
        }
        T::read_words(&words)
    }
}
pub fn read_words_into_vec<T: Readable>(words: &[&str], line: &str) -> Result<Vec<T::Output>, String> {
    let n = T::WORD_COUNT;
    assert_eq!(words.len() % n, 0);
    let mut result = Vec::new();
    for chunk in words.chunks(n) {
        match T::read_words(chunk) {
            Ok(v) => result.push(v),
            Err(msg) => {
                let fragment_msg = if n == 1 {
                    format!("word {}", result.len())
                } else {
                    let l = result.len();
                    format!("words {}-{}", n*l + 1, (n+1) * l)
                };
                return Err(format!(
                    "{} of line `{}`: {}", fragment_msg, line, msg
                ));
            }
        }
    }
    Ok(result)
}
pub fn split_into_words_for_collection<T: Readable>(
    line: &str, prefix_words_count: usize
) -> Result<Vec<&str>, String> {
    let n = T::WORD_COUNT;
    let words = split_into_words(line);
    if words.len() < prefix_words_count {
        return Err(
            format!("line `{}` has {} words, expected at least {}",
                    line, words.len(), prefix_words_count)
        );
    }
    if (words.len() - prefix_words_count) % T::WORD_COUNT != 0 {
        return Err(
            format!("line `{}` has {} words, expected {} + {}",
                    line, words.len(), prefix_words_count, n)
        );
    }
    Ok(words)
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        readable_collection!($u: => $collection_in, $collection_out);
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl<$u: Readable> ReadableFromLine for $collection_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $collection_out;
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let words = split_into_words_for_collection::<$u>(line, 0)?;
                Ok(read_words_into_vec::<$u>(&words, line)?.into_iter().collect())
            }
        }
        impl<T1: Readable, $u: Readable> ReadableFromLine for (T1, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = T1::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let val1 = T1::read_words(&words[..prefix_len])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, $u: Readable> ReadableFromLine for (T1, T2, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::WORD_COUNT;
                let val3 = T3::read_words(&words[start .. start+count3])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, rest.into_iter().collect()))
            }
        }
        impl<T1: Readable, T2: Readable, T3: Readable, T4: Readable, $u: Readable> ReadableFromLine for (T1, T2, T3, T4, $collection_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T1::Output, T2::Output, T3::Output, T4::Output, $collection_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let prefix_len = <(T1, T2, T3, T4)>::WORD_COUNT;
                let words = split_into_words_for_collection::<$u>(line, prefix_len)?;
                let mut start = 0;
                let count1 = T1::WORD_COUNT;
                let val1 = T1::read_words(&words[start .. start+count1])?;
                start += count1;
                let count2 = T2::WORD_COUNT;
                let val2 = T2::read_words(&words[start .. start+count2])?;
                start += count2;
                let count3 = T3::WORD_COUNT;
                let val3 = T3::read_words(&words[start .. start+count3])?;
                start += count3;
                let count4 = T4::WORD_COUNT;
                let val4 = T4::read_words(&words[start .. start+count4])?;
                let rest = read_words_into_vec::<$u>(&words[prefix_len..], line)?;
                Ok((val1, val2, val3, val4, rest.into_iter().collect()))
            }
        }
    };
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty $(,)* ) => {
        let $pat = read::<$t>();
    };
    ( ! $(,)* ) => {
        let _ = read::<()>();
    };
    ( $pat:pat = $t:ty, $( $rest:tt )+ ) => {
        read_inner!($pat = $t; $($rest)+);
    };
    ( !, $( $rest:tt )+ ) => {
        read_inner!(_ = (); $($rest)+);
    };
}
#[macro_export]
#[doc(hidden)]
macro_rules! read_inner {
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; !, $( $rest:tt )* ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ; $($rest)*);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; $pat:pat = $t:ty ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , $pat = $t ;);
    };
    ( $( $acc_pat:pat = $acc_t:ty ),+ ; ! ) => {
        read_inner!($( $acc_pat = $acc_t ),+ , _ = () ;);
    };
    ( $( $pat:pat = $t:ty ),+ ; ) => {
        let ($($pat),+) = read::<($($t),+)>();
    };
}
pub trait ReadableFromChunk {
    type Output;
    fn lines_count() -> usize;
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String>;
}
impl<T1: ReadableFromLine, T2: ReadableFromLine> ReadableFromChunk for (T1, T2) {
    type Output = (T1::Output, T2::Output);
    fn lines_count() -> usize { 2 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        Ok((out1, out2))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine> ReadableFromChunk for (T1, T2, T3) {
    type Output = (T1::Output, T2::Output, T3::Output);
    fn lines_count() -> usize { 3 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        Ok((out1, out2, out3))
    }
}
impl<T1: ReadableFromLine, T2: ReadableFromLine, T3: ReadableFromLine, T4: ReadableFromLine> ReadableFromChunk for (T1, T2, T3, T4) {
    type Output = (T1::Output, T2::Output, T3::Output, T4::Output);
    fn lines_count() -> usize { 4 }
    fn read_chunk(lines: &[String]) -> Result<Self::Output, String> {
        let out1 = T1::read_line(&lines[0])?;
        let out2 = T2::read_line(&lines[1])?;
        let out3 = T3::read_line(&lines[2])?;
        let out4 = T4::read_line(&lines[3])?;
        Ok((out1, out2, out3, out4))
    }
}
pub fn read_chunk<T: ReadableFromChunk>() -> T::Output {
    let stdin = std::io::stdin();
    let mut handle = stdin.lock();
    read_chunk_from_handle::<T>(&mut handle).unwrap()
}
fn read_chunk_from_handle<T: ReadableFromChunk>(handle: &mut std::io::StdinLock) -> Option<T::Output> {
    use std::io::BufRead;
    let mut lines = vec![String::new(); T::lines_count()];
    let mut first = true;
    for line in &mut lines {
        if handle.read_line(line).unwrap() == 0 && first {
            return None;
        }
        first = false;
    }
    Some(T::read_chunk(&lines).unwrap())
}
#[macro_export]
macro_rules! read_chunk {
    ( $( $pat:pat = $t:ty ),+ ) => {
        let ($($pat),+) = read_chunk::<($($t),+)>();
    };
}
static mut STDIN: Option<std::io::Stdin> = None;
pub struct ReadLines<T: ReadableFromLine> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromLine> Iterator for ReadLines<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        use std::io::BufRead;
        let mut line = String::new();
        if self.lock.read_line(&mut line).unwrap() > 0 {
            Some(T::read_line(&line).unwrap())
        } else {
            None
        }
    }
}
pub fn read_lines<T: ReadableFromLine>() -> ReadLines<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadLines {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub struct ReadChunks<T: ReadableFromChunk> {
    lock: std::io::StdinLock<'static>,
    phantom: std::marker::PhantomData<T>
}
impl<T: ReadableFromChunk> Iterator for ReadChunks<T> {
    type Item = T::Output;
    fn next(&mut self) -> Option<T::Output> {
        read_chunk_from_handle::<T>(&mut self.lock)
    }
}
pub fn read_chunks<T: ReadableFromChunk>() -> ReadChunks<T> {
    unsafe {
        if STDIN.is_none() {
            STDIN = Some(std::io::stdin());
        }
    }
    ReadChunks {
        lock: unsafe { STDIN.as_ref().unwrap().lock() },
        phantom: std::marker::PhantomData::<T>
    }
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET utils
#[macro_export]
macro_rules! echo {
    () => {
        println!()
    };
    ($e: expr $(,)?) => {
        println!("{}", $e)
    };
    ($e: expr, $($es: expr),+ $(,)?) => {
        {
            use std::io::Write;
            let stdout = std::io::stdout();
            let mut handle = stdout.lock();
            write!(handle, "{}", $e).unwrap();
            $(
                write!(handle, " {}", $es).unwrap();
            )+
            writeln!(handle).unwrap();
        }
    };
}
pub fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}
#[allow(non_snake_case)]
pub fn YN(result: bool) {
    if result {
        println!("YES");
    } else {
        println!("NO");
    }
}
pub fn exit(msg: impl std::fmt::Display) -> ! {
    println!("{}", msg);
    std::process::exit(0)
}
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// SNIPPET cmp
use std::cmp::{Ord, Ordering};
pub fn minmax<T: Ord>(a: T, b: T) -> (T, T) {
    if a <= b { (a, b) } else { (b, a) }
}
#[macro_export]
macro_rules! chmin {
    ($place: expr, $expr: expr) => {
        let value = $expr;
        if value < $place {
            $place = value;
        }
    }
}
#[macro_export]
macro_rules! chmax {
    ($place: expr, $expr: expr) => {
        let value = $expr;
        if value > $place {
            $place = value;
        }
    }
}
#[derive(Clone, Copy, PartialEq, Eq, Debug, Default, Hash)]
pub struct Reverse<T: Ord>(pub T);
impl<T: Ord> PartialOrd for Reverse<T> {
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Reverse<T> {
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
pub trait SortDesc<T> {
    fn sort_desc(&mut self) where T: Ord;
    fn sort_desc_by<F>(&mut self, cmp: F)
    where
        F: FnMut(&T, &T) -> std::cmp::Ordering;
    fn sort_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, key: F);
    fn sort_unstable_desc(&mut self) where T: Ord;
    fn sort_unstable_desc_by<F>(&mut self, cmp: F)
    where
        F: FnMut(&T, &T) -> std::cmp::Ordering;
    fn sort_unstable_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, key: F);
}
impl<T> SortDesc<T> for [T] {
    fn sort_desc(&mut self) where T: Ord {
        self.sort_by(|x, y| y.cmp(x));
    }
    fn sort_desc_by<F>(&mut self, mut cmp: F)
    where
        F: FnMut(&T, &T) -> std::cmp::Ordering
    {
        self.sort_by(|x, y| cmp(y, x));
    }
    fn sort_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, mut key: F) {
        self.sort_by_key(|x| Reverse(key(x)));
    }
    fn sort_unstable_desc(&mut self) where T: Ord {
        self.sort_unstable_by(|x, y| y.cmp(x));
    }
    fn sort_unstable_desc_by<F>(&mut self, mut cmp: F)
    where
        F: FnMut(&T, &T) -> std::cmp::Ordering
    {
        self.sort_unstable_by(|x, y| cmp(y, x));
    }
    fn sort_unstable_desc_by_key<K: Ord, F: FnMut(&T) -> K>(&mut self, mut key: F) {
        self.sort_unstable_by_key(|x| Reverse(key(x)));
    }
}
#[derive(Clone, Copy, PartialEq, PartialOrd, Debug, Default, Hash)]
pub struct Total<T: PartialOrd + PartialEq>(pub T);
impl<T: PartialOrd + PartialEq> Eq for Total<T> {}
impl<T: PartialOrd + PartialEq> Ord for Total<T> {
    fn cmp(&self, other: &Self) -> Ordering {
        self.partial_cmp(other).unwrap()
    }
}
pub trait IteratorMinmax: Iterator {
    fn minmax(self) -> Option<(Self::Item, Self::Item)>;
    fn minmax_by_key<K, F>(self, key_fn: F) -> Option<(Self::Item, Self::Item)>
    where
        K: Ord,
        F: FnMut(&Self::Item) -> K;
    fn minmax_by<F>(self, compare: F) -> Option<(Self::Item, Self::Item)>
    where
        F: FnMut(&Self::Item, &Self::Item) -> Ordering;
}
impl<T: Ord + Clone, I: Iterator<Item=T>> IteratorMinmax for I {
    fn minmax(self) -> Option<(Self::Item, Self::Item)> {
        self.minmax_by(|a, b| a.cmp(b))
    }
    fn minmax_by_key<K, F>(self, mut key_fn: F) -> Option<(Self::Item, Self::Item)>
    where
        K: Ord,
        F: FnMut(&Self::Item) -> K
    {
        self.minmax_by(|a, b| key_fn(a).cmp(&key_fn(b)))
    }
    fn minmax_by<F>(mut self, mut compare: F) -> Option<(Self::Item, Self::Item)>
    where
        F: FnMut(&Self::Item, &Self::Item) -> Ordering
    {
        let first = self.next()?;
        let second = match self.next() {
            Some(x) => x,
            None => return Some((first.clone(), first))
        };
        let mut result = minmax(first, second);
        while let Some(x) = self.next() {
            let (min, max) = result;
            result = if compare(&x, &min) == Ordering::Less {
                (x, max)
            } else if compare(&max, &x) == Ordering::Less {
                (min, x)
            } else {
                (min, max)
            };
        }
        Some(result)
    }
}
pub trait WithCmpIdentity<T>: Sized {
    fn new(x: T) -> Self;
    fn inf() -> Self;
    fn as_option(&self) -> Option<&T>;
    fn as_option_mut(&mut self) -> Option<&mut T>;
    fn into_option(self) -> Option<T>;
    fn is_fin(&self) -> bool {
        self.as_option().is_some()
    }
    fn is_inf(&self) -> bool {
        self.as_option().is_none()
    }
    fn expect_fin(self, msg: &str) -> T {
        self.into_option().expect(msg)
    }
    fn fin(self) -> T {
        self.into_option().unwrap()
    }
    fn fin_or(self, default: T) -> T {
        self.into_option().unwrap_or(default)
    }
    fn fin_or_else<F: FnOnce() -> T>(self, f: F) -> T {
        self.into_option().unwrap_or_else(f)
    }
    fn map_or<U, F: FnOnce(T) -> U>(self, default: U, f: F) -> U {
        self.into_option().map_or(default, f)
    }
    fn map_or_else<U, D, F>(self, default: D, f: F) -> U
    where
        D: FnOnce() -> U,
        F: FnOnce(T) -> U
    {
        self.into_option().map_or_else(default, f).into()
    }
}
#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
pub enum MaybeNegInf<T> {
    Inf,
    Fin(T)
}
pub type Max<T> = MaybeNegInf<T>;
#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
pub enum MaybeInf<T> {
    Fin(T),
    Inf
}
pub type Min<T> = MaybeInf<T>;
macro_rules! impl_with_cmp_identity {
    ($t:ident) => {
        impl<T> $t<T> {
            pub fn map<U: Ord, F: FnOnce(T) -> U>(self, f: F) -> $t<U> {
                match self {
                    $t::Fin(x) => $t::Fin(f(x)),
                    $t::Inf => $t::Inf
                }
            }
        }
        impl<T> WithCmpIdentity<T> for $t<T> {
            fn new(x: T) -> $t<T> { $t::Fin(x) }
            fn inf() -> $t<T> { $t::Inf }
            fn as_option(&self) -> Option<&T> {
                match self {
                    $t::Fin(x) => Some(x),
                    $t::Inf => None
                }
            }
            fn as_option_mut(&mut self) -> Option<&mut T> {
                match self {
                    $t::Fin(x) => Some(x),
                    $t::Inf => None
                }
            }
            fn into_option(self) -> Option<T> {
                match self {
                    $t::Fin(x) => Some(x),
                    $t::Inf => None
                }
            }
        }
    }
}
impl_with_cmp_identity!(MaybeNegInf);
impl_with_cmp_identity!(MaybeInf);

// END SNIPPETS
// Here is the documentation: https://yoshrc.github.io/rust-atcoder-snippets/atcoder_snippets/index.html

fn dfs(v: usize, adj: &[Vec<usize>], full: &mut [bool]) {
    if full[v] {
        return;
    }
    full[v] = true;
    for &next in &adj[v] {
        dfs(next, adj, full);
    }
}

fn main() {
    read!(n = usize, h = usize, w = usize);
    let mut cards: Vec<_> = read_lines::<(usize_, usize_, u64)>().collect();
    cards.sort_desc_by_key(|&(_y, _x, a)| a);
    let mut vs = VecUnionFindSets::with_items(h + w);
    let mut adj = vec![Vec::new(); h + w];
    let mut full = vec![false; h + w];
    let mut ans = 0;
    for (y, x, a) in cards {
        let x = h + x;
        if full[y] && full[x] {
            continue;
        }
        ans += a;

        if full[y] {
            dfs(x, &adj, &mut full);
        } else if full[x] {
            dfs(y, &adj, &mut full);
        } else if vs.unite(y, x).unwrap() {
            adj[y].push(x);
            adj[x].push(y);
        } else {
            dfs(y, &adj, &mut full);
        }
    }
    echo!(ans);
}