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)

def input_from_console():
    n = int(input())
    return n


def factor(n):
    factors = []
    tmp = n
    if tmp == 1:
        return [1]
    prime_max = int(n ** (1 / 2.0)) + 1
    i = 2

    while tmp > i:
        if tmp % i == 0:
            factors.append(i)
            tmp = int(tmp / i)
        else:
            i += 1
            if i > prime_max:
                factors.append(tmp)
                return factors
    factors.append(tmp)
    return factors


def multiplyList(myList):
    result = 1
    for x in myList:
        result = result * x
    return result


def solve(n):
    factors = factor(n)
    # print(factors)
    if len(factors) == 1:
        return factors[0] - 1
    else:
        sum_max = multiplyList(factors[0:len(factors)-1]) + multiplyList(factors[len(factors)-1:]) - 2
        # print(multiplyList(factors[0:len(factors)-1]), '*', multiplyList(factors[len(factors)-1:]))
        for i in range(len(factors)):
            sum_tmp = multiplyList(factors[0:i]) + multiplyList(factors[i:]) - 2
            # print(sum_max, sum_tmp)
            if sum_tmp >= sum_max:
                return sum_max
    return 0


def main():
    n = input_from_console()
    print(solve(n))


if __name__ == "__main__":
    import sys

    if sys.gettrace():  # Check if the python interpreter is in debug mode or not.
        check_cases()
    else:
        main()