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)

n = int(input())

def prime_decomposition(n):
    i = 2
    table = []
    while i * i <= n:
        while n % i == 0:
            n = int(n/i)
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
    return table

l = prime_decomposition(n)
l.append(1)
l.reverse()
a = 1
b = 1

for i in range(len(l)):
    if a <= b:
        a *= l[len(l)-1-i]
    else:
        b *= l[len(l)-1-i]

print(a+b-2)