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)

n = gets.chomp.to_i
divisor = []
i = 1
while i * i <= n
    if n % i == 0 then
        divisor << i
        tmp = n / i
        divisor << tmp if tmp != i
    end
    i += 1
end
divisor.sort!
divisor_num = divisor.size

if divisor_num & 1 == 1 then
    puts (divisor[divisor_num/2] - 1) * 2
else
    puts divisor[divisor_num/2] + divisor[divisor_num/2-1] - 2
end