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 (2.7.1) (judge verdict: Accepted)

n = gets.chomp.to_i

rn = Math.sqrt(n).to_i + 1
arr = []
arr2 = []
(1..rn).each { |num|
    arr << num if n % num == 0
}

arr.each { |num|
    arr2 << n / num
}

m = arr.zip(arr2).map { |a1, a2|
    (a1 - 1) + (a2 - 1)
}.min

puts m