Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List
import Control.Monad.ST
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

newUF n = VUM.replicate n (-1 :: Int)

root uf x = do
    p <- VUM.read uf x
    if p < 0
        then return x
        else do
            r <- root uf p
            VUM.write uf x r
            return r

same uf x y = liftM2 (==) (root uf x) (root uf y)

unite uf x y = do
    px <- root uf x
    py <- root uf y
    when (px /= py) $ do
        sx <- VUM.read uf px
        sy <- VUM.read uf py
        let (par, chld) = if sx < sy then (px, py)　else (py, px)
        VUM.write uf chld par
        VUM.write uf par (sx + sy) 

size uf x = do
    px <- root uf x
    s <- VUM.read uf px
    return $ abs s
readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    [n,m] <- getIntList
    ab <- replicateM m $ do
        [a,b] <- getIntList
        return (a-1,b-1)
    
    let vec = VU.create $ do
        uf <- newUF n
        forM_ ab $ \(a,b) -> do
            unite uf a b
        return uf
    let ans = abs $ VU.minimum vec
    print ans