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 (2.7.1) (judge verdict: Accepted)

require 'pp'
require 'prime'

$DEBUG ? define_method(:dpp){|e|pp e} : define_method(:dpp){|e|}

# 入力値を数値で返却する
def gets_i()
  gets.chomp.to_i
end
n = gets_i
max = (n ** 0.5).ceil
min = n
1.upto(max) do |i|
  if n % i == 0
    min = [min, i + n / i - 2].min
  end
end

puts min