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 (3.8.2) (judge verdict: Accepted)

N = int(input())

def low_divisors(N):
  K=1
  low_divs = []
  while K*K <= N:
    if N%K == 0:
      low_divs.append(K)
    K += 1

  return low_divs

L_divs = low_divisors(N)
D = []

for i in range(len(L_divs)):
  D.append(L_divs[i]+N//L_divs[i])
  
print(min(D)-2)