Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

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

module Main where

import qualified Data.ByteString.Char8         as BS
import           Data.List
import           Data.Char
import           Control.Arrow
import qualified Data.IntSet                   as IntSet
import qualified Data.Vector.Unboxed           as VU

main :: IO ()
main = do
  [n] <- unfoldr (BS.readInteger . BS.dropWhile isSpace) <$> BS.getLine
  print $ solve n
 where
  solve n = minimum
    $ map (\x -> if mod n x == 0 then x - 1 + div n x - 1 else n) [1 .. sqn]
    where sqn = floor $ sqrt $ fromIntegral n