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: Wrong Answer)

#include <iostream>
#include <vector>
#include <math.h>
#include <algorithm>
#include <string>
#include <map>
#include <iomanip>
#define rep(i,N) for(int i=0; i<N;i++)
using namespace std;

int main(){
    long int N,ans1,ans2;
    long int k=1;
    cin >>N;
    for(long int j=(long int)sqrt(N);j>0;j--){
        cout <<j<<endl;
        if(N%j==0){
            ans1=N/j;
            ans2=j;
            break;
        }
    }
    cout <<ans1+ans2-2<<endl;
    return 0;
}