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)

import sys
from itertools import permutations

N = int(input())
val = []
i = 2

while i * i <= N:
    while N % i == 0:
        N //= i
        val.append(i)
    i += 1
if N > 1:
    val.append(N)

a, b = 1, 1
for i in val[0::2]:
    a *= i
for i in val[1::2]:
    b *= i

a, b = 0, 0
max0 = 0
for i in permutations(val):
    max1 = 1
    max2 = 1
    for j in i[0::2]:
        max1 *= j
    for j in i[1::2]:
        max2 *= j
    if max0 == 0 or abs(max1 - max2) < max0:
        max0 = abs(max1 - max2)
        a = max1
        b = max2
    
print(a + b - 2)