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: Runtime Error)

import numpy as np
import math

def pk(n):
  b = 2
  fct = []
  while b * b <= n:
    while n % b == 0:
      n //= b
      fact.append(b)
    b += 1
  if n > 1:
    fct.append(n)
  return fct

n = int(input())
temp = np.prod(pk(n))
sqi = int(math.sqrt(temp))
while 1:
  if temp % sqi 1= 0:
    sqi += 1
  else:
    break
i = sqi
j = temp // sqi
print(i + j -2)