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)

MOD=10**9+7
cnt=0; sum=0; prev=nil; can=true; h=Hash.new(0)
def gs() gets.chomp end
def gi() gets.to_i end
def gsmi() gets.chomp.split.map(&:to_i) end

def desc(ar) ar.sort!{|x,y|y<=>x} end
def min(a,b) a<=b ? a : b end
def max(a,b) a>=b ? a : b end
def sum(ar) ar.inject(:+) end

def C(a,b) b==0||a==b ? 1 : (b=a-b if a/2<b;(a-b+1..a).inject(:*)/(1..b).inject(:*)) end

def puts_yesno(can) puts(can ? 'Yes' : 'No') end
def putsend(s) puts s; exit end
def debug(k,v) puts "#{k}:#{v}" end
########### ( ˘ω˘ )ｽﾔｧ… ###########
n=gi

require 'prime'

ar=[]
np=n.prime_division
# np.each do |a,b|
#   temp=[1]
#   b.times do |i|
#     temp<<a*(i+1)
#   end
#   ar<<temp
# end

def div(pr,k=0)
  Enumerator.new do |en|
    if pr.size == k
      en << 1
    else
      p,e = pr[k]
      div(pr,k+1).each do |d|
        (e+1).times do |e1|
          en << (p**e1) * d
        end
      end
    end
  end
end

divs=div(np).to_a.sort

#puts divs.to_s

sq=Math.sqrt(n).to_i
res=1
divs.each do |d|
  if d<=sq
    res=d
  else
    break
  end
end

puts res+(n/res)-2