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)

import sys
import math

def is_prime(num):
	if num == 1:
		return False
	for i in range(2, int(math.sqrt(num)) + 1):
		if num % i == 0:
			return False
	return True

n = int(input())
ans = n
if is_prime(n) == True:
	print(n - 1)
else:
	for i in range(1, n + 1):
		for j in range(1, n + 1):
			if i * j == n:
				if ans > i + j:
					ans = (i - 1) + (j - 1)
print(ans)