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: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define int  long long
#define tc(t)  int t; cin>>t; while(t--)
#define f(n)    for(int i=0;i<n;i++)
#define endl   "\n"
int32_t main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n;
    cin>>n;
    if(n==1) {
        cout<<"0"<<endl;
        return 0;
    }
    if(n==2)
    {
        cout<<"1"<<endl;
        return 0;
    }
    int a=1;
    int b=1;
    for(int i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            a=i;
            b=n/i;
        }


    }
    if(a==1&&b==1)
    {
        a=n;
        b=1;
    }
    //cout<<a<<" "<<b<<endl;
    cout<<(a+b-2)<<endl;


}