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 divisors(n):
    ret = set()

    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            ret.add(i)
            ret.add(n // i)
    return ret

div_lis = sorted(list(divisors(n)))

if len(div_lis) % 2 == 0:
    print(div_lis[(len(div_lis) - 1) // 2] + div_lis[(len(div_lis) + 1) // 2] - 2)
else:
    print(div_lis[len(div_lis) // 2] * 2 - 2)