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.to_i

primes = Prime.prime_division(N).map{|a,b|[a]*b}.flatten
a, b = 1,1
sum =[1]
dp = Array.new(primes.size + 1){ {} }
dp[0][0] = [1,1]
primes.each_with_index do |prime, i|
  sum[i+1] = sum[i] * prime
  (i+2).times do |j|
    if j == 0
      dp[i+1][j] = [dp[i][j][0], dp[i][j][1] * prime]
    elsif !dp[i][j]
      dp[i+1][j] = [dp[i][j-1][0]*prime, dp[i][j-1][1]]
    else
      if (dp[i][j][0] + dp[i][j][1] * prime) < (dp[i][j-1][0] *prime + dp[i][j-1][1])
        dp[i+1][j] = [dp[i][j][0], dp[i][j][1] * prime]
      else
        dp[i+1][j] = [dp[i][j-1][0]*prime, dp[i][j-1][1]]
      end
    end
  end
end
res = dp[-1].values.map{|a| a[0]+a[1]}.min
puts res - 2