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<math.h>
long long int keta(long long int n){
  long long int i=0;
  while(n){
    n/=10;
    i++;
  }
  return i-1;
}
long long int root(long long int n){
  long long int i=1,j,s;
  /*j=keta(n)-1;
  j/=2;
  while(j){
    i*=10;
  }*/
  while(i*i<n){
    s=++i;
  }
//  printf("%lld",s);
  return s;
}
int main(void){
  long long int n,i,c=1,d=1;
//  double a;
  scanf("%lld",&n);
  //a=(double)n;
  //a=sqrt(a);
  for(i=root(n);i>=2;i--){
    if(n%i==0){
      c=i;
      break;
    }
  }
  d=n/c;
  printf("%lld\n",d+c-2);
  return 0;
}