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 8.8.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine

getRoot :: Int -> Int -> Int -> Int
getRoot n r s
  | r^2 > n = s
  | n `mod` r == 0 = getRoot n (r+1) (r + n `div` r - 2)
  | otherwise = getRoot n (r + 1) s

main = do
  n <- getInt
  print $ getRoot n 1 0