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 F first
#define S second
#define pb push_back
#define f(i,x,n) for(int i=x;i<n;i++)
#define all(c) c.begin(),c.end()
#define int ll
using ll = long long;
using pii = pair<int,int>;
const int MOD = 1e9+7, N = 1e5 + 10; 

int32_t main(){
   ios::sync_with_stdio(false);
   cin.tie(NULL);
   int n;
   cin >> n;
   int ans = 1e18;
   for(int i=1;i*i<=n;i++){
      if(n%i==0){
         ans = min(ans,i-1+n/i-1);
      }
   }
   cout << ans << '\n';
   return 0;
}