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 (3.8.2) (judge verdict: Time Limit Exceeded)

from operator import mul
from functools import reduce
import itertools
import copy

N = int(input())

# N = i*jをみつける
# (i, j)


def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

def remove_dup_list(tmplist):
    return map(list, set(map(tuple, tmplist)))


prime_list = prime_factorize(N)

if len(prime_list)<=1:
    result = N-1
else:
    result = 10**12


#print(prime_list)
for i in range(len(prime_list)//2):
    # i個抽出
    tmp = list(itertools.combinations(prime_list, i+1))
    tm = remove_dup_list(map(list, tmp))
    #print(tm)
    for _ in tm:
        temp_origin_list = copy.copy(prime_list)
        for item in _:
            temp_origin_list.remove(item)
        result = min(result, reduce(mul, _) + reduce(mul, temp_origin_list) - 2)

print(result)