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)

"use strict";

function divisor(num) {
  let curDiv = 1;
  const midian = parseInt(num) / 2;
  for (let i = 2; i < midian; i++) {
    if (num % i === 0 && i > curDiv) {
      curDiv = i;
    }
  }
  return curDiv;
}

function main(input) {
  input = parseInt(input.split("\n")[0]);
  console.log(input);
  let divis = divisor(input);
  console.log(divis - 1 + input / divis - 1);
}

main(require("fs").readFileSync("/dev/stdin", "UTF-8"));