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)

# https://atcoder.jp/contests/abc144/tasks/abc144_c
# -*- coding: utf-8 -*-

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

input_val = int(input())
a = prime_factorize(input_val)

cnt_odd = 0
cnt_eve = 0

if len(a) == 0:
    print(0)
elif len(a) == 1:
    print(a[0]-1)
else:
    cnt_odd = a[0]
    cnt_eve = a[1]
    for i in range(2, len(a)):
        if i % 2 == 0:
            cnt_odd *= a[i]
        else:
            cnt_eve *= a[i]
    print(cnt_odd-1 + cnt_eve-1)