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
primes = []
divisors = []

array = Prime.prime_division(n)
array.each do |a, b|
  b.times do
    primes.push(a)
  end
end

(1..primes.size).each do |i|
  primes.combination(i) do |prime|
    divisors << prime.inject{|a,b| a *= b}
  end
end

divisors.uniq!

result = n
flag = true
divisors.each do |d|
  if result > n / d + d
    result = n / d + d

    if d == 1 || n / d == 1
      flag = true
    else
      flag = false
    end
  end
end

puts flag ? result - 1 : result - 2