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: Wrong Answer)

function Main(n) {
  var s = Math.floor(Math.sqrt(n));
	var r = 0;
	var result = Array();
	for (var i = 2;i <= s;i++) {
		if ((n % i) == 0) {
			r = 0;
			do {
				r++; 
				n = n / i;
			} while ((n % i) == 0);
			result.push({num:i, r:r});
		}
	}
	if (n > s) {
		result.push({num:n, r:1});
	}
  result.reverse();
  var P = 1;0
  var Q = 1;
for(var i = 0;i<result.length;i++){
  for(var j = 0;j<result[i].r;j++){
if(P<Q){
  P *= result[i].num;
}else{
  Q *= result[i].num;
}
  }
}
  console.log(P+Q-2);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));