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: Accepted)

require 'pp'
require 'prime'
require 'set'

N=gets.chomp.split(' ').map{|n| n.to_i}.first

if Prime.prime?(N)
  puts N-1
  exit
end

a=0
b=0

mini = 1_000_000_000_000_0
source = Math.sqrt(N).to_i+1
1.upto(source) do |n|
  next if N%n!=0
  a=n
  b=N/n
  if ((a-1 + b-1) < mini)
    mini = a-1 + b-1
  end
end

puts mini