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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
typedef long long ll;

ll ft_sqrt(ll n)
{
	ll i = 1;
	ll cnt = 0;
	while (i <= n)
	{
		if (i % 2)
		{
			n -= i;
			cnt++;
		}
		i++;
	}
	return (cnt);
}

int main(void)
{
	ll N;
	scanf("%lld", &N);
	ll i = 1;
	ll a;
	ll b;
	while (i <= (ll)sqrt((double)N))
	{
		if (N % i == 0)
			a = i;
		i++;
	}
	b = N / a;
	printf("%lld", (a+b) - 2);
	return (0);
}