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 PyPy3 (7.3.0) (judge verdict: Accepted)

import math

N = int(input())
even = False

if N % 2 == 0:
    even = True

factor1 = int(math.floor(N ** (1/2)))

# if even:  # Nが偶数の時はfactor1を偶数にしておく
#     if factor1 % 2 == 1:
#         factor1 -= 1
# else:
#     if factor1 % 2 == 0:
#         factor1 -= 1

while True:
    if N % factor1 == 0:
        factor2 = int(N / factor1)
        break
    else:
        factor1 -= 1

print(factor1 + factor2 - 2)