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.to_i
m = n
divs = []
while m % 2 == 0 do
  divs.push(2)
  m /= 2
end
d = 3
while d * d <= m do
  if m % d == 0
    divs.push(d)
    m /= d
  else
    d += 2
  end
end
divs.push(m) if m > 1
min_move = n - 1
for i in 0...(2 ** divs.size) do
  a = 1
  b = 1
  for j in 0...divs.size do
    if (i >> j) & 1 == 0
      a *= divs[j]
    else
      b *= divs[j]
    end
  end
  move = (a - 1) + (b - 1)
  min_move = move if min_move > move
end
puts min_move