Problem:
Score : 500 points

Problem Statement

There are N cards placed face down in a row. On each card, an integer 1 or 2 is written.

Let A_i be the integer written on the i-th card.

Your objective is to guess A_1, A_2, ..., A_N correctly.

You know the following facts:

For each i = 1, 2, ..., M, the value A_{X_i} + A_{Y_i} + Z_i is an even number.

You are a magician and can use the following magic any number of times:

Magic: Choose one card and know the integer A_i written on it. The cost of using this magic is 1.

What is the minimum cost required to determine all of A_1, A_2, ..., A_N?

It is guaranteed that there is no contradiction in given input.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq X_i < Y_i \leq N

1 \leq Z_i \leq 100

The pairs (X_i, Y_i) are distinct.

There is no contradiction in input. (That is, there exist integers A_1, A_2, ..., A_N that satisfy the conditions.)

Input

Input is given from Standard Input in the following format:

N M
X_1 Y_1 Z_1
X_2 Y_2 Z_2
\vdots
X_M Y_M Z_M

Output

Print the minimum total cost required to determine all of A_1, A_2, ..., A_N.

Sample Input 1

3 1
1 2 1

Sample Output 1

2

You can determine all of A_1, A_2, A_3 by using the magic for the first and third cards.

Sample Input 2

6 5
1 2 1
2 3 2
1 3 3
4 5 4
5 6 5

Sample Output 2

2

Sample Input 3

100000 1
1 100000 100

Sample Output 3

99999

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;
use std::collections::HashSet;

pub trait Readable {
    type Output;
    fn words_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;
            fn words_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;
    fn words_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>;
    fn words_count() -> usize {
        1
    }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
macro_rules ! impl_readable_for_ints { ( $ ( $ t : ty ) * ) => { $ ( impl Readable for $ t { type Output = Self ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( words [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse \"{}\" as {}" , words [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_readable_for_ints ! ( i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64 ) ;
macro_rules ! define_one_origin_int_types { ( $ new_t : ident $ int_t : ty ) => { # [ doc = " Converts 1-origin integer into 0-origin when read from stdin." ] # [ doc = "" ] # [ doc = " # Example" ] # [ doc = "" ] # [ doc = " ```no_run" ] # [ doc = " # #[macro_use] extern crate atcoder_snippets;" ] # [ doc = " # use atcoder_snippets::read::*;" ] # [ doc = " // Stdin: \"1\"" ] # [ doc = " read!(a = usize_);" ] # [ doc = " assert_eq!(a, 0);" ] # [ doc = " ```" ] # [ allow ( non_camel_case_types ) ] pub struct $ new_t ( ) ; impl Readable for $ new_t { type Output = $ int_t ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { <$ int_t >:: read_words ( words ) . map ( | n | n - 1 ) } } } ; ( $ new_t : ident $ int_t : ty ; $ ( $ inner_new_t : ident $ inner_int_t : ty ) ;* ) => { define_one_origin_int_types ! ( $ new_t $ int_t ) ; define_one_origin_int_types ! ( $ ( $ inner_new_t $ inner_int_t ) ;* ) ; } ; }
define_one_origin_int_types ! ( u8_ u8 ; u16_ u16 ; u32_ u32 ; u64_ u64 ; usize_ usize ) ;
macro_rules ! impl_readable_for_tuples { ( $ t : ident $ var : ident ) => ( ) ; ( $ t : ident $ var : ident ; $ ( $ inner_t : ident $ inner_var : ident ) ;* ) => { impl_readable_for_tuples ! ( $ ( $ inner_t $ inner_var ) ;* ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,*> Readable for ( $ t , $ ( $ inner_t ) ,* ) { type Output = ( <$ t >:: Output , $ ( <$ inner_t >:: Output ) ,* ) ; fn words_count ( ) -> usize { let mut n = <$ t >:: words_count ( ) ; $ ( n += <$ inner_t >:: words_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { let mut start = 0 ; let $ var = <$ t >:: read_words ( & words [ start .. start +<$ t >:: words_count ( ) ] ) ?; start += <$ t >:: words_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: read_words ( & words [ start .. start +<$ inner_t >:: words_count ( ) ] ) ?; start += <$ inner_t >:: words_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } ; }
impl_readable_for_tuples ! ( T4 x4 ; T3 x3 ; T2 x2 ; T1 x1 ) ;
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_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::words_count() {
            return Err(format!(
                "line \"{}\" has {} words, expected {}",
                line,
                words.len(),
                T::words_count()
            ));
        }
        T::read_words(&words)
    }
}
impl<T: Readable> ReadableFromLine for Vec<T> {
    type Output = Vec<T::Output>;
    fn read_line(line: &str) -> Result<Self::Output, String> {
        let n = T::words_count();
        let words = split_into_words(line);
        if words.len() % n != 0 {
            return Err(format!(
                "line \"{}\" has {} words, expected multiple of {}",
                line,
                words.len(),
                n
            ));
        }
        let mut result = Vec::new();
        for chunk in words.chunks(n) {
            match T::read_words(chunk) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    let flagment_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 \"{}\": {}", flagment_msg, line, msg));
                }
            }
        }
        Ok(result)
    }
}
impl<T: Readable, U: Readable> ReadableFromLine for (T, Vec<U>) {
    type Output = (T::Output, <Vec<U> as ReadableFromLine>::Output);
    fn read_line(line: &str) -> Result<Self::Output, String> {
        let n = T::words_count();
        #[allow(deprecated)]
        let trimmed = line.trim_right_matches('\n');
        let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ').collect();
        if words_and_rest.len() < n {
            return Err(format!(
                "line \"{}\" has {} words, expected at least {}",
                line,
                words_and_rest.len(),
                n
            ));
        }
        let words = &words_and_rest[..n];
        let empty_str = "";
        let rest = words_and_rest.get(n).unwrap_or(&empty_str);
        Ok((T::read_words(words)?, Vec::<U>::read_line(rest)?))
    }
}
macro_rules ! impl_readable_from_line_for_tuples_with_vec { ( $ t : ident $ var : ident ) => ( ) ; ( $ t : ident $ var : ident ; $ ( $ inner_t : ident $ inner_var : ident ) ;+ ) => { impl_readable_from_line_for_tuples_with_vec ! ( $ ( $ inner_t $ inner_var ) ;+ ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,+ , U : Readable > ReadableFromLine for ( $ t , $ ( $ inner_t ) ,+ , Vec < U > ) { type Output = ( $ t :: Output , $ ( $ inner_t :: Output ) ,+ , Vec < U :: Output > ) ; fn read_line ( line : & str ) -> Result < Self :: Output , String > { let mut n = $ t :: words_count ( ) ; $ ( n += $ inner_t :: words_count ( ) ; ) + # [ allow ( deprecated ) ] let trimmed = line . trim_right_matches ( '\n' ) ; let words_and_rest : Vec <& str > = trimmed . splitn ( n + 1 , ' ' ) . collect ( ) ; if words_and_rest . len ( ) < n { return Err ( format ! ( "line \"{}\" has {} words, expected at least {}" , line , words_and_rest . len ( ) , n ) ) ; } let words = & words_and_rest [ .. n ] ; let empty_str = "" ; let rest = words_and_rest . get ( n ) . unwrap_or ( & empty_str ) ; let ( $ var , $ ( $ inner_var ) ,* ) = < ( $ t , $ ( $ inner_t ) ,+ ) >:: read_words ( words ) ?; Ok ( ( $ var , $ ( $ inner_var ) ,* , Vec ::< U >:: read_line ( rest ) ? ) ) } } } ; }
impl_readable_from_line_for_tuples_with_vec ! ( T4 t4 ; T3 t3 ; T2 t2 ; T1 t1 ) ;
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 > ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } ; }
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        }).collect();
    result
}
#[macro_export]
macro_rules ! readx_loop { ( |$ pat : pat = $ t : ty | $ body : expr ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } ; ( |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readx_loop ! ( | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin
        .lock()
        .lines()
        .take(n)
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        }).collect();
    if result.len() < n {
        panic!(
            "expected reading {} lines, but only {} lines are read",
            n,
            result.len()
        );
    }
    result
}
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr , |$ pat : pat = $ t : ty | $ body : expr ) => { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; { let mut lock = stdin . lock ( ) ; for _ in 0 ..$ n { let mut line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } } ; ( $ n : expr , |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readn_loop ! ( $ n , | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
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()
    }
}

pub struct HashUnionFindSets<T: Eq + std::hash::Hash + std::fmt::Debug> {
    items: std::collections::HashMap<T, UnionFindNode<T>>,
}
#[derive(Clone)]
enum UnionFindNodeInner<T: Eq + std::hash::Hash> {
    Root { len: usize },
    Child { parent: UnionFindNode<T> },
}
#[derive(Clone)]
struct UnionFindNode<T: Eq + std::hash::Hash>(
    std::rc::Rc<std::cell::RefCell<UnionFindNodeInner<T>>>,
    T,
);
impl<T: Eq + std::hash::Hash + Clone> UnionFindNode<T> {
    fn new(item: T) -> UnionFindNode<T> {
        UnionFindNode(
            std::rc::Rc::new(std::cell::RefCell::new(UnionFindNodeInner::Root { len: 1 })),
            item,
        )
    }
}
impl<T: Eq + std::hash::Hash> std::cmp::PartialEq for UnionFindNode<T> {
    fn eq(&self, other: &UnionFindNode<T>) -> bool {
        self.1 == other.1
    }
}
impl<T: Eq + std::hash::Hash> std::cmp::Eq for UnionFindNode<T> {}
impl<T: Eq + std::hash::Hash> std::hash::Hash for UnionFindNode<T> {
    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
        self.1.hash(state);
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> HashUnionFindSets<T> {
    pub fn new() -> HashUnionFindSets<T> {
        HashUnionFindSets {
            items: std::collections::HashMap::new(),
        }
    }
    fn error_msg(items: &[&T]) -> 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(&mut self, item: T) -> bool {
        if self.items.contains_key(&item) {
            false
        } else {
            self.items.insert(item.clone(), UnionFindNode::new(item));
            true
        }
    }
    pub fn items_len(&self) -> usize {
        self.items.len()
    }
    fn find(&self, item: &T) -> Option<(UnionFindNode<T>, usize)> {
        fn go<T: Eq + std::hash::Hash + Clone>(
            node: UnionFindNode<T>,
        ) -> (UnionFindNode<T>, usize) {
            let inner = node.0.as_ref().clone().into_inner();
            match inner {
                UnionFindNodeInner::Root { len } => (node, len),
                UnionFindNodeInner::Child { parent } => {
                    let (root, len) = go(parent);
                    let mut borrowed = node.0.borrow_mut();
                    *borrowed = UnionFindNodeInner::Child {
                        parent: root.clone(),
                    };
                    (root, len)
                }
            }
        }
        self.items.get(item).cloned().map(go)
    }
    pub fn len_of(&self, item: &T) -> Result<usize, String> {
        self.find(item)
            .map(|(_, len)| len)
            .ok_or_else(|| HashUnionFindSets::error_msg(&[item]))
    }
    pub fn set_eq(&self, item1: &T, item2: &T) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some((root1, _)), Some((root2, _))) => Ok(root1 == root2),
            (Some(_), None) => Err(HashUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(HashUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(HashUnionFindSets::error_msg(&[item1, item2])),
        }
    }
    pub fn unite(&mut self, item1: &T, item2: &T) -> Result<bool, String> {
        match (self.find(item1), self.find(item2)) {
            (Some((root1, len1)), Some((root2, len2))) => {
                if root1 == root2 {
                    Ok(false)
                } else {
                    let (mut root, mut child, root_node) = if len1 < len2 {
                        (root2.0.borrow_mut(), root1.0.borrow_mut(), &root2)
                    } else {
                        (root1.0.borrow_mut(), root2.0.borrow_mut(), &root1)
                    };
                    *root = UnionFindNodeInner::Root { len: len1 + len2 };
                    *child = UnionFindNodeInner::Child {
                        parent: root_node.clone(),
                    };
                    Ok(true)
                }
            }
            (Some(_), None) => Err(HashUnionFindSets::error_msg(&[item2])),
            (None, Some(_)) => Err(HashUnionFindSets::error_msg(&[item1])),
            (None, None) => Err(HashUnionFindSets::error_msg(&[item1, item2])),
        }
    }

    pub fn get_sets(&self) -> Vec<HashSet<&T>> {
        let mut map = HashMap::new();
        for item in self.items.keys() {
            let node = self.find(&item).unwrap().0;
            map.entry(node).or_insert(HashSet::new()).insert(item);
        }
        map.into_iter().map(|(_, v)| v).collect()
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> std::fmt::Debug for HashUnionFindSets<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        use std::collections::{HashMap, HashSet};
        let mut root_to_set = HashMap::new();
        for item in self.items.keys() {
            let root = self.find(item);
            let set = root_to_set.entry(root).or_insert(HashSet::new());
            set.insert(item);
        }
        let sets: Vec<HashSet<&T>> = root_to_set.into_iter().map(|(_, v)| v).collect();
        if sets.len() == 0 {
            write!(f, "{{}}")
        } else {
            write!(f, "{{{:?}", sets[0])?;
            for set in &sets[1..] {
                write!(f, ", {:?}", set)?;
            }
            write!(f, "}}")
        }
    }
}
impl<T: Eq + std::hash::Hash + std::fmt::Debug + Clone> std::iter::FromIterator<T>
    for HashUnionFindSets<T>
{
    fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> HashUnionFindSets<T> {
        HashUnionFindSets {
            items: iter
                .into_iter()
                .map(|x| (x.clone(), UnionFindNode::new(x)))
                .collect(),
        }
    }
}

fn main() {
    read!(n = usize, _ = ());
    let pairs = readx::<(usize_, usize_, String)>();
    let mut sets: HashUnionFindSets<usize> = (0..n).collect();
    for (a, b, _) in pairs {
        sets.unite(&a, &b).unwrap();
    }
    let ans = sets.get_sets().len();
    println!("{}", ans);
}