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 make_divisors(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)
	
	divisors.sort()
	return divisors

div = make_divisors(N)
if len(div) % 2 == 0:
	ind_2 = len(div) // 2
	ind_1 = ind_2 - 1
	print(div[ind_1] + div[ind_2] -2)
else:
	ind = len(div) // 2
	print(div[ind] * 2 -2)