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<iostream>
#include<math.h>
#include<vector>
#include<array>
#include<algorithm>
#include<numeric>
#include<map>
#include<queue>
#include<deque>
#include<set>
#include<cstdio>
#include<cstring>
#include<string>
using namespace std;
typedef long long ll;
typedef vector<int> vec;
typedef vector<vector<int>> mat;

int main(){
    ll N;cin>>N;
    ll M=sqrt(N)/1;
    while(M>0){
        ll n=N;
        if(n%M==0){
            cout<<M+n/M-2<<endl;
            return 0;
        }
        M--;
    }
    return 0;
}