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;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 10000000000000000




int main(){
    
	long long N;
	cin>>N;
	
	vector<long long> Y;
	
	for(long long i=1;i*i<=N;i++){
		if(N%i==0){
			Y.push_back(i);
			Y.push_back(N/i);
		}
	}
	
	long long ans = Inf;
	
	for(int i=0;i<Y.size();i++){
		long long a = Y[i];
		long long b = N/Y[i];
		ans = min(ans,a-1+b-1);
	}
	
	cout<<ans<<endl;
	
    return 0;
}