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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); i++)
#define repd(i,a,b) for (int i = (a); i < (b); i++)
typedef long long ll;
int main(void)
{
	ll N, min_sum=10000000000000, a, b;
	cin >> N;
	for(ll i = 1; i<=N/i; i++)
	{
		if (N%i==0)
		{
			if (min_sum>i+N/i)
			{
				a = i;
				b = N/i;
			}
		}
	}
	cout << (a-1)+(b-1) << endl;
}