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)

let scan_int () = Scanf.scanf " %d" (fun x -> x)
let print_int n = Printf.printf "%d\n" n

let rec solve i n ans =
  if i * i > n then ans
  else
    if n mod i = 0 then solve (i+1) n (min ans (i + (n/i) - 2))
    else solve (i+1) n ans

let init_val = int_of_float 1e12

let () =
  let n = scan_int() in
  print_int (solve 1 n init_val)