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

if Prime.prime?(n) then puts n-1
else

isBreak = false
i = 1
j = 1

cnt = 0
while true do
cnt_k = 0
while cnt_k<=cnt do
  if (i+cnt_k)*(j+cnt-cnt_k)==n then
    isBreak = true
    break
  end
  cnt_k += 1
end
break if isBreak
cnt += 1
end

puts cnt
end