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>
#define int long long int
#define mod 1000000007
#define pb push_back
#define pf push_front
#define ulli unsigned long long int
#define what_is(x) cerr << #x << " is " << x << endl;
#define pi 2*acos(0.0)
#define F  first
#define S  second
//#define endl '\n'
#define all(x) x.begin(),x.end()
using namespace std;
const int INF = 1e18L+5;
/*
int power(int x,int y)
{
	int res=1;
	while(y>0)
	{
		if(y%2==1)
			res=(res*x)%mod;
		x=(x*x)%mod;
		y=y/2;
	}
	return res;
}
*/
int32_t main()
{
	//cout.precision(10);
	//cout.setf(ios::fixed,ios::floatfield);
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	//freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	int T=1;
	//cin>>T;
	while(T--)
	{
		int n,ans=INF,a=INF,b=INF,i;
		cin>>n;
		for(i=1;i*i<=n;i++)
		{
			if(n%i==0)
			{
				a=i;
				b=n/i;
				if(ans>a+b-2)
				{
					ans=a+b-2;
				}
			}
		}
		cout<<ans<<endl;
	}
}