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 Ruby (2.3.3) (judge verdict: Runtime Error)

N = gets.to_i

ans = N - 1
f = Prime.prime_division(N)

dfs = lambda { |d, i|
  0.upto(f[i][1]) do |n|
    x = d
    x *= f[i][0] * n if n != 0
    if i == f.size - 1
      a = (x - 1) + (N / x - 1)
      ans = a if a < ans
    else 
      dfs.call(x, i + 1)
    end
  end
}

dfs.call(1, 0)
puts ans