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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  
  integer(16) :: i,j,n,m,l,p=0,q=0
  
  read(*,*)n
  m = int(sqrt(real(n)))
  do i = 1, m
    l = n/i
    if (i*l == n) then
      p = i
      q = l
    end if
  end do
  write(*,'(i0)')p+q-2
end program main