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)

def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0:
        cnt+=1
        temp //= i
      for j in range(cnt) :
        arr.append(i)

  if temp!=1:
    arr.append(temp)

  if arr==[]:
    arr.append(n)

  return arr

N = int(input())
fact = factorization(N)
fact.sort()

# print(fact)

while len(fact) > 4 :
  a = fact.pop(0)
  b = fact.pop(0)
  fact.append(a*b)
  fact.sort()

if len(fact) == 4 :
  x = fact.pop(0) * fact.pop(-1)
  y = fact.pop(0) * fact.pop(-1)
  fact.append(x)
  fact.append(y)
elif len(fact) == 3 :
  x = fact.pop(0) * fact.pop(-1)
  fact.append(x)

# print(fact)
if len(fact) == 1 :
  print(fact[0]-1)
else :
  print(fact[0]+fact[1]-2)