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)

n = gets.chomp.to_i
a = 0
b = 0
c = 1
d = []
i = 0
s = [] 
ans = 0
while true
  i += 1
  c = 1
  b = n / i
  c = n % i
  if c == 0
    s << b
    d << i
  end
  break if b == 0
end
s.reverse!
d.reverse!
if s.length > 2
  ans = s.length / 2
  ans = (s[ans]- 1 )+ (d[ans]- 1)
else
  ans = (s[0]- 1 )+ (d[0]- 1)
end
puts ans