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 OCaml (4.02.3) (judge verdict: Accepted)

open Scanf ;;
open Printf ;;

let divisors n =
  let rec f i =
    if i * i > n then []
    else if n mod i = 0 then i :: f (i + 1)
    else f (i + 1)
  in
  f 1
  ;;

let min_list a = List.fold_left min max_int a ;;

let () =
  let n = scanf "%d" (fun x -> x) in
  let ans = divisors n |> List.map (fun x -> x + n / x - 2) |> min_list in
  printf "%d\n" ans
  ;;