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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
def divisor_list(num):
  ans = []
  for i in range(1, int(num**0.5)+1):
    if num % i == 0:
      ans.append(i)
      if i != num // i:
        ans.append(num//i)
  return ans
d_list = sorted(divisor_list(N))
d_list = d_list[1:]

for i in d_list:
  for j in d_list:
    if N == i*j:
      print(i-1+j-1)
      break
  else:
    continue
  break