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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input) {
		input = input.split(" ");
		const num = parseInt(input[0], 10);
		var min = 0;
		var res = 0;
		for (i = 1; i <= Math.sqrt(num); i++) {
				if (num % i == 0) {
						if (min == 0 || (i - 1) + (num / i - 1) < min) {
								res = i + (num / i) - 2;
								min = res;
						}
				}
		}
		console.log(res);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));