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.util.Scanner;

public class Main {

	public static void main(String[] args) {

		/*
		 * Scannerで値取得。
		 */
		Scanner snum = new Scanner(System.in);

		//値取得
		long numN = snum.nextLong();

		snum.close();

		long tate = 0;
		long yoko = 0;

		//		numNを割る
		long halfLong = (long) (Math.sqrt(numN));

		//		halfLongの値から1ずつデクリメントしながら割り切れる値を探す
		//		割り切れたら割る→縦横の和から２引く
		for (tate = halfLong; tate > 0; tate--) {
			if (numN % tate == 0) {
				yoko = numN / tate;
				System.out.println(tate + yoko - 2);
				break;
			}
		}
	}

}