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: Wrong Answer)

import sys
input = sys.stdin.readline


def main():
    sc = Scan()
    n = sc.intarr()[0]
    minimum = n
    for i in range(1, n//2):
        if n % i == 0:
            cost = (n//i) + i-2
            if cost < n:
                minimum = cost
    print(minimum)


class Scan():

    def intarr(self):
        self.line = input()
        array = self.line.split(' ')
        num_array = [int(n) for n in array]
        return num_array

    def strarr(self):
        self.line = input()
        array = self.line.split(' ')
        array[-1] = array[-1].strip('\n')
        return array


main()