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

int main()
{
  long long int input;
  long long int i,j;
  scanf("%lld",&input);
  
  long long int minimum = 10000000000000;
  long long int i_min=0;
  long long int j_min=0;
  for(i=1;i<=sqrt(input);i++){
    if( (input%i)==0 ){
      j = input/i;
      //printf("%lld %lld\n",i,j);
      if( (i+j)<minimum ){
        
        minimum = i+j;
        i_min = i;
        j_min = j;
        //printf("%lld %lld %lld\n",i_min,j_min,minimum);
        
      }
    }
    else{
      continue; 
    }
  }

  
 
  
  printf("%lld\n",i_min+j_min-2);
             
  
  
  return 0; 
}