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()
{
  long int a,b,t,min,n;
  scanf("%ld",&n);
  min=n-1;
  for(a=2; a<=(sqrt(n)); a++){
    if(n%a==0){
      b=n/a;
      t=a+b-2;
      if(min>t)
        min=t;
    }
  }
  printf("%ld",min);
  return 0;
}