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 ll long long 
#define ull unsigned long long 
#define f(i,x,n) for(ll int i=x;i<n;i++) 
#define re(j,x,n) for(ll int j=x;j>=n;j--)
#define f1(k,x,n) for(ll int k=x;k<=n;k++)
#define mp make_pair
#define pb push_back
#define mod 1000000007
#define MAX 1000001
using namespace std;
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll int n;
    cin>>n;
    ll int mn=n-1;
    f1(i,2,sqrt(n))
    {
      if(n%i==0)
      { 
      	if(mn<(i-1)+((n/i)-1))
      		break;
      	mn=min(mn,(i-1)+((n/i)-1));
      }
    }
    cout<<mn;
}