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,a,b,c,m,sum;
    scanf("%lld", &N);
    m=N+1;
    a=sqrt(N);
    for(i=a;i>=1;i--){
        if(N%i==0){
            b=N/i;
            c=b+i;
            if(c<=m){
                m=c;
                sum=m-2;
            }
        }
    }
    printf("%lld\n", sum);
    return 0;
}