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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
typedef long long  ll ;
typedef double db;
const double pi = 3.141592654;
#define pb         push_back
#define forab(i,a,b)       for(int i=(a);i<=(b);i++)
#define CIN	ios_base::sync_with_stdio(0); cin.tie(0)
#define pcase(z,x)     printf("Case %ld: %lld\n",z,x)
#define nw	 "\n"
#define mod 1000000007


int main(void)
{
	CIN;
	ll tc,l,k=0,sum=0,x=0,y,z=0,m=1,n=0,ans=0,cnt=0;
	cin>>n;
	ll mx=1e16;
	for(ll i=1;i<=n;i++)
	{
		if(n%i==0){
			z=(i*i+n-2*i)/i;
			mx=min(mx,z);
		}
	}
	cout<<mx;
}