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: Time Limit Exceeded)

#include<stdio.h>
#include<string.h>
int primefn(long long a);
int main()
{
    long long N,i,j,mul1,mul2;
    int ans;
    scanf("%lld",&N);
    ans=primefn(N);
    if(ans==1)
    {
        printf("%lld",N-1);
        return 0;
    }
    i=1;
    j=N;
    mul1=N;
    for(;;)
    {
        mul2=i+j-2;
        if(mul2<mul1)
        {
            i++;
            for(;N%i!=0;i++)
            {
            }
            j=N/i;
            mul1=mul2;
        }
        else if(mul2>=mul1)
            break;

    }
    printf("%lld",mul1);
    return 0;
}
int primefn(long long a)
{
    long long k;
    for(k=2;k<=a/2;k++)
    {
        if(a%k==0)
            return 0;
    }
    return 1;
}