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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

bool IsPrime(long int num)
{
    if (num < 2) return false;
    else if (num == 2) return true;
    else if (num % 2 == 0) return false;

    double sqrtNum = sqrtl(num);
    for (long int i = 3; i <= sqrtNum; i += 2)
    {
        if (num % i == 0)
        {
            return false;
        }
    }

    return true;
}

int main(void){
    long int N, K;
    long int min = 0;

	cin >> N;
    min = N-1;

    if(IsPrime(N) == true){
        cout << (N-1) << endl;
        return 0;
    }

    for (long int i = 2; i < (N / 2); i++)
    {
        if ((N % i) == 0)
        {
            K = N / i;
            if ((i + K - 2) < min)
            {
                min = i + K - 2;
            }
            if(K <= i){break;}
        }
    }
    cout << min << endl;
    return 0;
}