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>

long sqrt(long p){
  int i,a=0;
  long m=0;
  for(i=62;i>=0;i-=2){
    a=(a<<2)|((p>>i)&3);
    m<<=1;
    if(a-m-1>=0){
      a-=m+1;
      m|=2;
    }
  }
  return(m>>1);
}

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