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 <iostream>
#include <vector>
#include <algorithm>
#include <math.h>
using namespace std;
typedef long long int ll;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	ll n; cin >> n;
	ll cp=n;
	for(ll i=2;i*i<=cp;i++){
		if(cp%i==0){
			while(cp%i==0){
				cp/=i;
				if(cp==1)break;
			}
			if(cp==1)break;
		}
	}
	if(cp==n){
		cout << n-1 << endl;
		return 0;
	}
	for(ll i=sqrtl(n);i>=i;i--){
		if(n%i==0){
			cout << i-1+n/i-1 << endl;
			return 0;
		}
	}
}