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: Wrong Answer)

require 'prime'

N = gets.chomp.to_i
divs = Prime.prime_division(N).to_a
primes = divs.flat_map {|v, n| Array.new(n, v)}

min = Float::INFINITY
ans = -Float::INFINITY
combination_size_max = divs.map(&:last).reduce(:+) / 2

if combination_size_max.zero?
  puts(N - 1)
  exit
end

cache = {}
sqrt = Math.sqrt(N)

(1..combination_size_max).each do |combination_size|
  primes.combination(combination_size).each do |combination|
    a = combination.reduce(:*)
    next if cache[a]
    cache[a] = true
    f = (sqrt - a).abs
    if f < min
      b = N / a
      ans = a.pred + b.pred
      min = f
    end
  end
end

puts ans