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)

a = int(input())

n =a
b = []
for i in range(2,int(-(-a**0.5//1))+1):
    if a % i ==0:
        b.append(i)
        a = a/i
        while a%i==0:
            b.append(i)
            a = a/i
if a != 1:
    b.append(a)
if b == []:
    b.append(a)

if len(b)==1:
    print(int(b[0]-1))
elif len(b)==2:
    print(int(b[0]+b[1]-2))
else:
    r = b[-1]
    s = b[-2]
    for j in range(2,len(b)):
        i = -1-j
        if r>s and s*b[i]>n/r/b[i]:
            s = s*b[i]
        else:
            r = r * b[i]
    print(int(r+s-2))