Problem:
Score : 500 points

Problem Statement

You are given a sequence (P_1,P_2,...,P_N) which is a permutation of the integers from 1 through N.
You would like to sort this sequence in ascending order by repeating the following operation:

Choose an element in the sequence and move it to the beginning or the end of the sequence.

Find the minimum number of operations required.
It can be proved that it is actually possible to sort the sequence using this operation.

Constraints

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

(P_1,P_2,...,P_N) is a permutation of (1,2,...,N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1
:
P_N

Output

Print the minimum number of operations required.

Sample Input 1

4
1
3
2
4

Sample Output 1

2

For example, the sequence can be sorted in ascending order as follows:

Move 2 to the beginning. The sequence is now (2,1,3,4).

Move 1 to the beginning. The sequence is now (1,2,3,4).

Sample Input 2

6
3
2
5
1
4
6

Sample Output 2

4

Sample Input 3

8
6
3
1
2
7
4
8
5

Sample Output 3

5

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

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE RecordWildCards       #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}

import           Control.Applicative
import           Control.DeepSeq
import           Control.Exception
import           Control.Monad
import           Control.Monad.ST
import           Control.Monad.Trans.State.Strict
import           Data.Array.Base
import           Data.Array.ST                    (STUArray, runSTUArray)
import           Data.Bits
import           Data.Bool
import qualified Data.ByteString.Char8            as B
import           Data.Char
import           Data.Coerce
import qualified Data.Foldable                    as F
import           Data.Function
import           Data.Int
import qualified Data.IntMap.Strict               as IM
import qualified Data.IntSet                      as IS
import qualified Data.List                        as L
import qualified Data.Map.Strict                  as M
import           Data.Monoid
import           Data.Ord
import qualified Data.Set                         as S
import           Data.STRef
import           Data.Tuple
import           Data.Word
import           Debug.Trace
import           GHC.Arr                          (Array, Ix (..), STArray)
import           GHC.Exts
import           System.Exit
import           System.IO

main :: IO ()
main = do
    n <- readLn :: IO Int
    xs <- L.unfoldr (B.readInt.B.dropWhile isSpace) <$> B.getContents
    print $ solve n xs

solve :: Int -> [Int] -> Int
solve n xs = go IM.empty xs
  where
    go :: IM.IntMap Int -> [Int] -> Int
    go !m (x:xs) = case IM.lookup (x - 1) m of
        Just len -> go (IM.insert x (len + 1) $ IM.delete (x - 1) m) xs
        Nothing  -> go (IM.insert x 1 m) xs
    go m [] = (n - ). maximum.map snd $ IM.toAscList m