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: Time Limit Exceeded)

require 'prime'
N = gets.to_i
pd = N.prime_division
ns = [1] + pd.flat_map { |n, e| [n] * e }.sort

def dfs(ns, i, a = 1, b = 1)
  if i == ns.size
    return (a - 1) + (b - 1)
  end
  [
    dfs(ns, i + 1, a * ns[i], b),
    dfs(ns, i + 1, a, b * ns[i])
  ].min
end

ans = dfs(ns, 0)
puts ans