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)

isPrime :: Int -> Bool
isPrime n = loop n 2
    where
        loop :: Int -> Int -> Bool
        loop n i
            | n <= 1 = False
            | n `rem` i == 0 = False
            | n < i * i = True
            | otherwise = loop n (i + 1)

solve :: Int -> Int
solve n 
    | isPrime n = n - 1
    | s * s == n = s * 2 -2
    | otherwise = s * 2 - 1
    where
        s :: Int
        s = floor . sqrt . fromIntegral $ n


main = do
    n <- readLn :: IO Int
    print $ solve n