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: Time Limit Exceeded)

import math

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors

N = int(input())

# 全部はいらないのでざっくりフィルタ
# lim = int(math.sqrt(N)) + 1
lim = (N // 2 ) + 1

min_count = 99999999999999999999
# 約数列挙してからのほうが早いか？
divisors = make_divisors(N)
for i in divisors :
    for k in divisors :
        if (i*k == N) :
            c = (i-1) + (k-1)
            if (c < min_count ) :
                min_count = c


# for i in range(1,lim+1) :
#     for k in range(1,lim+1) :
#         if (i*k == N) :
#             c = (i-1) + (k-1)
#             if (c < min_count ) :
#                 min_count = c

print(min_count)