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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h> 

using namespace std;


int main()
{
long long int n;
set<long long int>arr;
cin>>n;


for (int i=1; i<=sqrt(n); i++) 
	{ 
		if (n%i == 0) 
		{ 
			if (n/i == i)
			{
				arr.insert(i);
			}
			else
			{
				arr.insert(i);
				arr.insert(n/i);
			} 
	} 
	}

int j = ceil(arr.size()/2);

//cout<<endl<<j;

std::set<long long int>::iterator it = arr.begin();
std::advance(it, j);
long long int x = *it;
cout<<(x-1)+((n/x)-1);
}