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 <math.h>
int main()
{
   long long int N, i, j, sum=0, sum2=0, flag;
    scanf("%lld", &N);// let's say N=50
    i=1;
    while( i<=sqrt(N)){
        if(N%i==0){
            j=N/i;

            sum = i + j; // at first sum is 5. then it becomes 27
            if(sum > sum2) //51>0. now sum is not bigger than sum2
                sum2 = sum; // now sum2 is 51
            else if(sum < sum2) //27 < 51
                sum2 = sum;// now sum2 becomes 27. after that sum2 becomes 15
        }
        i++;
    }
    printf("%lld", sum2-2);
    return 0;
}