Problem:
Score : 300 points

Problem Statement

We will call a string obtained by arranging the characters contained in a string a in some order, an anagram of a.

For example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.

Given are N strings s_1, s_2, \ldots, s_N. Each of these strings has a length of 10 and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Constraints

2 \leq N \leq 10^5

s_i is a string of length 10.

Each character in s_i is a lowercase English letter.

s_1, s_2, \ldots, s_N are all distinct.

Input

Input is given from Standard Input in the following format:

N
s_1
s_2
:
s_N

Output

Print the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Sample Input 1

3
acornistnt
peanutbomb
constraint

Sample Output 1

1

s_1 = acornistnt is an anagram of s_3 = constraint. There are no other pairs i, j such that s_i is an anagram of s_j, so the answer is 1.

Sample Input 2

2
oneplustwo
ninemodsix

Sample Output 2

0

If there is no pair i, j such that s_i is an anagram of s_j, print 0.

Sample Input 3

5
abaaaaaaaa
oneplustwo
aaaaaaaaba
twoplusone
aaaabaaaaa

Sample Output 3

4

Note that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}
module Main where

import Control.Arrow hiding ((+++))
import Control.Monad
import Control.Monad.ST
import Control.Monad.State.Strict
import Data.Char
import Data.Function
import Data.Graph
import Data.List
import qualified Data.Map.Strict as Map
import Data.Maybe
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as C
import qualified Data.ByteString.Unsafe as B
import qualified Data.ByteString.Builder as BSB
import System.IO (stdout)

type Parser a = C.ByteString -> Maybe (a, C.ByteString)

parseInt :: Parser Int
parseInt = C.readInt . C.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = runStateT $
    (,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
 
parseInt3 :: Parser (Int, Int, Int)
parseInt3 = runStateT $
    (,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)
 
parseInt4 :: Parser (Int, Int, Int, Int)
parseInt4 = runStateT $
    (,,,) <$> StateT (C.readInt . C.dropWhile isSpace)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)
        <*> StateT (C.readInt . B.unsafeTail)

-- prime means pred
parseInt' :: Parser Int
parseInt' = fmap (pred *** id) . parseInt

getInts :: IO [Int]
getInts = unfoldr parseInt <$> C.getLine

-- prime means pred
getInts' :: IO [Int]
getInts' = unfoldr parseInt' <$> C.getLine

getIntTuple :: IO (Int, Int)
getIntTuple = do
  a:b:_ <- getInts
  return (a, b)

-- prime means pred
getIntTuple' :: IO (Int, Int)
getIntTuple' = do
  a:b:_ <- getInts'
  return (a, b)

getIntTuple3 :: IO (Int, Int, Int)
getIntTuple3 = do
  a:b:c:_ <- getInts
  return (a, b, c)

getIntTuple4 :: IO (Int, Int, Int, Int)
getIntTuple4 = do
  a:b:c:d:_ <- getInts
  return (a, b, c, d)

getIntVec :: Int -> IO (U.Vector Int)
getIntVec n = U.unfoldrN n parseInt <$> C.getLine

-- prime means pred
getIntVec' :: Int -> IO (U.Vector Int)
getIntVec' n = U.unfoldrN n parseInt' <$> C.getLine

-- priority queue
-- https://stackoverflow.com/questions/6976559/comparison-of-priority-queue-implementations-in-haskell
--
data SkewHeap a = Empty
                | SkewNode a (SkewHeap a) (SkewHeap a)
                deriving (Show)

(+++) :: Ord a => SkewHeap a -> SkewHeap a -> SkewHeap a
heap1@(SkewNode x1 l1 r1) +++ heap2@(SkewNode x2 l2 r2) 
  | x1 >= x2   = SkewNode x1 (heap2 +++ r1) l1 
  | otherwise  = SkewNode x2 (heap1 +++ r2) l2
Empty +++ heap = heap
heap +++ Empty = heap

node :: a -> SkewHeap a
node x = SkewNode x Empty Empty

extractMax Empty = Nothing
extractMax (SkewNode x l r ) = Just (x , l +++ r )

fromList :: Ord a => [a] -> SkewHeap a
fromList = foldl' (+++) Empty . map node

foldSkewHeap :: b -> (a -> b -> b -> b) -> SkewHeap a -> b
foldSkewHeap c f = u
  where
    u Empty = c
    u (SkewNode a l r) = f a (u l) (u r)

sumSkewHeap :: SkewHeap Int -> Integer
sumSkewHeap = foldSkewHeap 0 (\a l r -> fromIntegral a + l + r)

---------------------------------------------------------

makeMap :: [U.Vector Char] -> Map.Map (U.Vector Char) (Int, Integer)
makeMap = foldl' (\m k -> snd $ Map.insertLookupWithKey (\_ _ (c,v) -> (c+1,v+fromIntegral c)) k (1,0) m) Map.empty

sumMap :: Map.Map (U.Vector Char) (Int, Integer) -> Integer
sumMap = Map.foldl' (\ttl (_, v) -> ttl + v) 0

main :: IO ()
main = do
  n <- readLn :: IO Int
  ss <- replicateM n (fmap (U.fromList . sort) getLine)
  -- print $ makeMap ss
  print $ sumMap $ makeMap ss