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<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<utility>
#include<tuple>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>

using namespace std;

using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

#define BIL ((ll)1e9)
#define MOD ((ll)1e9+7)
#define INF (1LL<<60)           //1LL<<63でオーバーフロー
#define inf (1<<29)             //1<<29でオーバーフロー

int main(int argc,char* argv[]){
    ll n;
    cin >> n;

    ll root=INF;
    for(ll i=1;i*i<=n;i++){
        if(n%i!=0){
            continue;
        }else{
            ll x=i-1,y=n/i-1;

            root=min(root,x+y);
        }
    }

    cout << root << endl;

    return 0;
}