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)

input = require('fs').readFileSync('/dev/stdin', 'utf8')
lines = input.split('\n')
N = lines.shift() * 1

_dividers = function(n) {
  var arr = []
  for (var i = 1; i*i <= n; i++) {
     if (n % i === 0) {
       arr.push(i)
       if ( i != n / i) {
         arr.push(n / i)
       }
     }
  }
  return arr.sort((a, b) => a - b)
}

ds = _dividers(N)

min = N
for (i=0; i <ds.length-i; i++) {
    for (j=i; j <ds.length; j++) {
        if (N == ds[i] * ds[j]) {
            if (min > ds[i] - 1 + ds[j] - 1) {
                min = ds[i] - 1 + ds[j] - 1
            }         
        }
    }
}
console.log(min)