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 <math.h>
#include <stdio.h>
#include <limits.h>

int main(void) {
    long long n, m;
    long long minimum = LLONG_MAX;

    scanf("%lld\n", &n);

    m = (long long) sqrt(n);

    for (long long i = 1; i <= m; i++) {
        long long a, b;
        if (n % i == 0) {
            a = n / i;
            b = (i - 1) + (a - 1);
            if (b < minimum) {
                minimum = b;
            }
        }
    }

    fprintf(stdout, "%lld\n", minimum);

    return 0;
}