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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.PrintStream;
import java.util.Scanner;

public class Main {
	static final PrintStream out = System.out;
	static final Scanner sc = new Scanner(System.in);
	static final long Mod = 1000_000_007L;
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		System.exit(0);
	}

	void solve() {
		long N = nextLong();
		long cnt = 0;
		//out.println(Math.sqrt(N));
		long x = (long) Math.sqrt(N);
		while(N % x != 0) {
			x--;
		}
		long y = N/x;
		cnt += (x - 1)+(y - 1);

		out.println(cnt);
	}


	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)a[i] = nextInt();
		return a;
	}
	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)a[i] = nextLong();
		return a;
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
	public long nextLong() {
		return Long.parseLong(next());
	}
	public String next() {
		return sc.next();
	}

	long gcd(long m,long n) {
		if (m<n) return gcd(n,m);
		if (n==0)return m;
		return gcd(n,m%n);
	}
}