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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>

int main(void){
    long long n=0;
    scanf("%ld",&n);
    //printf("%ld",n);
    
    long long a,b=0;
    long long s = floor(sqrt(n));
    int i = 0;
    for(i=s;i>=1;i--){
        if(n%i==0){
            a=i;
            b=n/i;
            printf("%ld\n",a+b-2);
            return 0;
        }
    }

}