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: Wrong Answer)

#include<stdio.h>
#include<math.h>
int main(void){
  int i,j=0,k=0;
  unsigned long a,b,n;

  scanf("%ld",&n);

  for(i=1;i<sqrt(n);i++){
    if(n%i==0){
      j++;
    }
  }
  printf("%d\n",j);

  for(i=1;k<j;i++){
    if(n%i==0){
      a=i;
      b=n/i;
      k++;
      printf("%ld %ld %d\n",a,b,k);
    }
  }
  printf("%ld\n",a+b-2);
  
  return 0;
}