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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())


from math import sqrt

def divisor(num):
    max_num = int(sqrt(num))
    divisor_list = []
    for i in range(1, max_num + 1):
        if num % i == 0:
            divisor_list.append(i)
            divisor_list.append(num//i)
    sorted_divisor_list = sorted(divisor_list)
    return sorted_divisor_list

def main():
    l = divisor(n)
    n_i = l[len(l)//2 - 1]
    n_j = l[len(l)//2]
    dist = n_i - 1 + n_j - 1
    print(dist)

main()