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: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
#include <stdlib.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);
}

ll common_maxl(ll n)
{
	ll i = 1;
	ll j = 1;
	ll logi = 1;
	ll logj = n;

	while (i <= ft_sqrt(n))
	{
		j = 1;
		while (j <= n)
		{
			if (i * j == n)
			{
				logi = i;
				logj = j; 
			}
			j++;
		}
		i++;
	}
	return (logi);
}

int main(void)
{
	ll N;
	scanf("%lld", &N);
	ll logi = common_maxl(N);
	ll I = logi - 1;
	ll logj;
	ll i = 1;
	while (i < N)
	{
		if (i * logi == N)
		{
			logj = i;
			break ;
		}
		i++;
	}
	ll J = logj - 1;
	printf("%lld", I+J);
	return (0);
}