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>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) < (b) ? (a) : (b))

#define scani(i) scanf("%d", &(i))
#define scanc(c) scanf("%c", &(c))
#define scand(d) scanf("%lf", &(d))

#define printi(i) printf("%d\n", (i))

#define NUM (100)

int main()
{
    long long int n;
    scanf("%lld", &n);
    
    double r = sqrt(n);
    long long int i = (long long int)r;
    if(i == 1){
        printf("%lld\n", n - 1);
        return 0;
    }
    
    while(n % i){
        i--;
    }
    
    long long int j = n / i;
    printf("%lld\n", i + j - 2);
    
    return 0;
}