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)

'use strict'

const Main = (input) => {
  const N = parseInt(input.trim())

  const divisors = []

  for (let i = 1; i <= Math.sqrt(N); i++) {
    if ((N % i) === 0) {
      divisors.push(i)
    }
  }

  const result = (N / Math.max.apply(null, divisors)) + Math.max.apply(null, divisors) - 2

  console.log(result)
  return result
}

Main(require('fs').readFileSync('/dev/stdin', 'utf8'))