Count the Palindromes Given a number n, calculate the amount of bases in the range of [2, n) in which b(n) is a Palindrome.

Example

n = 8 has the base conversions:

2 = 1000
3 = 22
4 = 20
5 = 13
6 = 12
7 = 11


Of which 2 of them, 3 = 22 and 7 = 11 are palindromes. So return 2. 

Clarifications


For the sake of convenience, Your answer only needs to be correct for inputs 3 - 36 inclusive, as few languages can handle base conversion of >36.
A single digit number is considered a palindrome.
This is sequence A135551 on OEIS


Test Cases

3   -&gt; 1
4   -&gt; 1
5   -&gt; 2
6   -&gt; 1
7   -&gt; 2
8   -&gt; 2
9   -&gt; 2
10  -&gt; 3
11  -&gt; 1
12  -&gt; 2
13  -&gt; 2
14  -&gt; 2
15  -&gt; 3
16  -&gt; 3
17  -&gt; 3
18  -&gt; 3
19  -&gt; 1
20  -&gt; 3
21  -&gt; 4
22  -&gt; 2
23  -&gt; 2
24  -&gt; 4
25  -&gt; 2
26  -&gt; 4
27  -&gt; 3
28  -&gt; 4
29  -&gt; 2
30  -&gt; 3
31  -&gt; 3
32  -&gt; 3
33  -&gt; 3
34  -&gt; 3
35  -&gt; 2
36  -&gt; 5


Finally


Standard Loopholes Apply.
This is code-golf, so fewest bytes wins.
Have Fun!
05AB1E, &nbsp;10&nbsp; 8 bytes

-2 bytes thanks to Emigna (use "bifurcation" instruction Â to replace duplicate and reverse DR &amp; increment the loop to avoid needing to close it.)

G¹N&gt;вÂQO


Try it online!

How?

G¹N&gt;вÂQO
G        - for N in range(1, input()+1):
 ¹       -   1st input
  N      -   N (the loop variable)
   &gt;     -   increment
    в    -   base conversion
     Â   -   push reverse
      Q  -   equal?
       O -   sum
         - print top of stack