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 fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define pb push_back 
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define pii pair<int,int>
#define ld long double
#define int long long int 
#define F first 
#define S second

signed main()
{
    fast;
    int n;
    cin>>n;
    int ans = 1e18;
    for(int i=1;i*i<=n;i++)
    {
        if(n%i==0)
        {
            int x = i;
            int y = n/i;
            ans = min(ans,abs(x-1)+abs(y-1));
        }
    }
    cout<<ans;
}