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: Wrong Answer)

factor :: Integer -> [Integer]
factor 1 = []
factor n = (prime:) . factor $ n `div` prime
  where divisors = dropWhile ((/=0) . mod n) [2..ceiling . sqrt $ fromIntegral n]
        prime = if null divisors
                then n
                else head divisors

solve :: Int -> [Integer] -> [Integer]
solve _ [a] = [a - 1]
solve 0 as = []
solve c as = x + y - 2 : solve (c - 1) as
  where x = product $ take c as
        y = product $ drop c as

main :: IO ()
main = do
  n <- readLn
  let res = factor n
  print . minimum $ solve (fromIntegral (length res - 1)) res