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: Runtime Error)

from enum import Enum
from queue import Queue

import numpy as np

import collections
import bisect
import sys
import math

from scipy.sparse.csgraph import floyd_warshall

BIG_NUM = 200000000000
MOD = 1000000007
EPS = 0.000000001

N = int(input())
ans = BIG_NUM

for i in range(0,int(np.sqrt(N))):
    if N % i == 0:
        j = N//i
        ans = min(ans, i+j-2)

print(ans)