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 ll long long int
#define ld long double
#define ff first
#define ss second
#define pb emplace_back
#define mp make_pair
#define MOD 1000000007
#define FAST ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);srand(time(NULL))
int main()
{
    ll n;
    cin>>n;
    ll ans = 1e18;
    for(ll i=1;i<=sqrt(n);i++)
    {
        if(n%i==0)
        {
            ans = min(ans,i+(n/i));
        }
    }
    ans -= 2;
    cout<<ans;
}