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>

int main(void){
    long long int n;
    scanf("%lld",&n);
    long long int x = 1, y = n;
    long long int i = 1, j = 1, id;
    double d = sqrt((double)n);
    id = (int)d;
    if(n % 2 != 0){
        j = 2;
    }
    while(i <= id){
        if(n % i == 0){
            if(x + y >= i + n/i){
                x = i;
                y = n / i;
            }
        }        
        if(x >= y || i >= y){
            break;
        }
        i += j;
    }
    printf("%lld\n",x+y-2);
    return 0;
}