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)

from functools import reduce
from operator import mul


def trial_division(n):
  factors = []
  f = 2
  while f**2 <= n:
    if n % f == 0:
      n //= f
      factors.append(f)
    else:
      f += 1
  if n != 1:
    factors.append(n)
  return factors

N = int(input())
factors = trial_division(N)

if len(factors) == 1:
  print(factors[0]-1)
else:
  res = N**2
  for i in range(len(factors)-1):
    a = reduce(mul, factors[:i+1])
    b = reduce(mul, factors[i+1:])
    if a+b-2 < res:
      res = a+b-2
  print(res)