You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}
{-# OPTIONS_GHC -fno-warn-unused-imports #-}
{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
{-# OPTIONS_GHC -fno-warn-unused-binds #-}
{-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
{-# LANGUAGE OverloadedStrings #-}
-- {-# LANGUAGE FlexibleContexts #-}
-- {-# LANGUAGE MultiWayIf #-}
-- {-# LANGUAGE BangPatterns #-}
-- {-# LANGUAGE ViewPatterns #-}
-- {-# LANGUAGE TupleSections #-}

import           System.IO hiding (char8)
import           Control.Applicative
import           Control.Monad
import           Data.List
import           Data.Tuple
import           Data.Int
import           Data.Char
import           Data.Function (on)
import           Data.Ord (comparing)
import           Data.Monoid (mappend)
import           Data.Array
-- import           Data.Array.Unboxed
-- import           Data.Array.IArray
-- import           Data.Array.ST
-- import           Data.Array.MArray
-- import           Data.Array.Unsafe
-- import           Data.Array.Base(unsafeRead, unsafeWrite)
-- import           Data.Array.IO
import           Data.Ix
import           Data.Maybe
-- import           Data.Monoid hiding ((<>))
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BL
import           Data.ByteString.Builder
import           Data.Graph
import           Data.Tree
-- import           Data.Vector.Unboxed ((//), (++), (!), (!?))
-- import qualified Data.Vector.Unboxed as U
-- import           Data.IntSet (IntSet)
-- import qualified Data.IntSet as IntSet
import           Data.IntMap.Strict (IntMap)
import qualified Data.IntMap.Strict as IntMap
import           Data.Sequence ((|>), (<|), (><),ViewR(..), ViewL(..), Seq)
import qualified Data.Sequence              as Seq
-- import           Data.Foldable (toList, minimumBy)
-- import           Debug.Trace

main = solve <$ getInt1 <*> getInts >>= print

solve :: [Int] -> Int
solve = sum . map cost . cycleNotation

cost :: [Int] -> Int
cost xs = minimum xs * (length xs - 2) + sum xs

cycleNotation :: [Int] -> [[Int]]
cycleNotation ns = filter ((1<) . length) . map flatten $ components graph where
  graph = buildG (minimum ns, maximum ns) . zip ns $ sort ns

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

getInt1 :: IO Int
getInt1 = readInt1 <$> BS.getLine

getInt2 :: IO (Int, Int)
getInt2 = readInt2 <$> BS.getLine

getInt3 :: IO (Int, Int, Int)
getInt3 = readInt3 <$> BS.getLine

getInts :: IO [Int]
getInts = readInts <$> BS.getLine

getIntN :: Int -> IO [Int]
getIntN n = map readInt1 <$> replicateM n BS.getLine

format :: Show a => Maybe a -> IO ()
format Nothing = putStrLn "NO"
format (Just a) = putStrLn "YES" >> print a

-- [1,2,3] -> 1 2 3
putInts :: [Int] -> IO ()
putInts [] = return ()
putInts xs = BL.putStrLn . toLazyByteString . foldl1 mappend . intersperse (char8 ' ') $ map intDec xs

readInt1 :: BS.ByteString -> Int
readInt1 = fst . fromJust . BS.readInt

readInt2 :: BS.ByteString -> (Int,Int)
readInt2 = toTuple . readInts

readInt3 :: BS.ByteString -> (Int,Int,Int)
readInt3 = toTriple . readInts

readInts :: BS.ByteString -> [Int]
readInts =  map readInt1 . BS.words

readInt641 :: BS.ByteString -> Int64
readInt641 = fromIntegral . fst . fromJust . BS.readInteger

readInt642 :: BS.ByteString -> (Int64,Int64)
readInt642 = toTuple . readInt64s

readInt643 :: BS.ByteString -> (Int64,Int64,Int64)
readInt643 = toTriple . readInt64s

readInt64s :: BS.ByteString -> [Int64]
readInt64s =  map readInt641 . BS.words

readInteger1 :: BS.ByteString -> Integer
readInteger1 = fst . fromJust . BS.readInteger

readInteger2 :: BS.ByteString -> (Integer,Integer)
readInteger2 = toTuple . readIntegers

readInteger3 :: BS.ByteString -> (Integer,Integer,Integer)
readInteger3 = toTriple . readIntegers

readIntegers :: BS.ByteString -> [Integer]
readIntegers =  map readInteger1 . BS.words

toTuple :: [a] -> (a, a)
toTuple [x, y] = (x, y)

toTriple :: [a] -> (a, a, a)
toTriple [x, y, z] =(x, y, z)

fromTuple :: (a, a) -> [a]
fromTuple (x, y) = [x, y]

fromTriple :: (a, a, a) -> [a]
fromTriple (x, y, z) = [x, y, z]

-- if not applying, use "const"

applyTuple :: (a -> a') -> (b -> b') -> (a, b) -> (a', b')
applyTuple f g (x, y) = (f x, g y)

applyTriple :: (a -> a') -> (b -> b') -> (c -> c') -> (a, b, c) -> (a', b', c')
applyTriple f g h (x, y, z) = (f x, g y, h z)

-- @since 4.8.0.0
sortOn' :: Ord b => (a -> b) -> [a] -> [a]
sortOn' f =
  map snd . sortBy (comparing fst) . map (\x -> let y = f x in y `seq` (y, x))