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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>
#include <string.h>
int fun(long long int x)
{
    for(long long int i=2;i*i<=x;i++)
    {
        if(x%i==0)
            return 0;
    }
    return 1;
}
int main()
{
    long long int n;
    scanf("%lld",&n);
    long long int x=sqrt(n);
    if(fun(n)==1)
    {
        printf("%lld",n-1);

    }
    else
    for(long long int i=x,j=x;;i++)
    {
        if(i*(long long int)(n/i)==n)
        {
            printf("%lld",i+(long long int)(n/i)-2);
            break;
        }
        if(j*(long long int)(n/j)==n)
        {
            printf("%lld",j+(long long int)(n/j)-2);
            break;
        }
        j--;
    }


}