Assume that you started to store items in progressively expanding square location, like this for the first 9 numbers:

```
05 04 03
06 01 02
07 08 09
```

And like this for the expanding to include up to the first 25 numbers:

```
17 16 15 14 13
18 05 04 03 12
19 06 01 02 11
20 07 08 09 10
21 22 23 24 25
```

You might easily notice that the first - and innermost - layer containes only one number (`01`), the second one  - immediately around it - contains 8 numbers (number in the `02-09` range) and so on.

Your task is to create a function that given a number `n` simply returns the number of layers required to store up to `n` (included).

```python
layers(1) == 1
layers(5) == 2
layers(25) == 3
layers(30) == 4
layers(50) == 5
```

**Fair warning:** you will always and only get positive integers, but be ready for bigger numbers in the tests!

If you had fun with this, also try some follow up kata: [progressive spiral number branch](https://www.codewars.com/kata/progressive-spiral-number-branch/) and [progressive spiral number distance](https://www.codewars.com/kata/progressive-spiral-number-distance/).

*[Base idea taken from [here](http://adventofcode.com/2017/day/3)]*

Difficulty: introductory

Starter code:

def layers(n):
	

Solutions:
from math import ceil, sqrt

def layers(n):
    return ceil(sqrt(n)) // 2 + 1

def layers(n):
    return (1 + (n-1)**.5) // 2 + 1

def layers(n):
    i = 1
    r = 1
    while i*i < n: 
        i += 2
        r += 1
        
    return r

import math
def layers(n):
    return math.ceil( (n**0.5 + 1.0)*0.5)

def layers(n):
    return int(((n - 1)**0.5 + 1) // 2) + 1 

from math import ceil
def layers(n):
    return ceil((n**.5+1)/2)

from itertools import count

def layers(n):
    for i in count(1):
        if n <= (2*i-1) ** 2:
            return i

from math import ceil

def layers(n):
    r = ceil(n**0.5)    
    return (r + (1 if r % 2 else 2)) // 2    

from math import ceil; layers=lambda n: ceil(n**0.5)//2+1

def layers (n):
    level, i = 1, 1
    continuer = True
    while continuer :
        x = i * i
        if x < n :
            level += 1
            i += 2
        elif n <= x:
            return level