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: Accepted)

N = int(input())

def judge(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n%i == 0:
      divisors.append(i)
      if i != n//i:
        divisors.append(n//i)
  return divisors

divisors = judge(N)
divisors.sort()
if len(divisors) % 2 == 0:
  while len(divisors) >= 3:
    divisors.pop(0)
    divisors.pop(-1)
  print(max(1, sum(divisors)-2))
else:
  while len(divisors) >= 2:
    divisors.pop(0)
    divisors.pop(-1)
  print(max(1, sum(divisors)*2-2))