Find the sum of all possible base representations The objective of this challenge is to write a program to convert an inputed string of what can be assumed as containing only letters and numbers from as many bases between 2 and 36 as possible, and find the base 10 sum of the results.

The input string will be converted to all the bases in which the number would be defined according to the standard alphabet for bases up to 36: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ. For example, the input 2T would be valid in only bases 30 and up. The program would convert 2T from bases 30 through 36 to decimal and sum the results.

You may assume that the input string contains only letters and numbers. Your program may use uppercase or lowercase; it can, but does not need to, support both.



Test cases

Sample input: 2T

Chart of possible bases

Base   Value
30     89
31     91
32     93
33     95
34     97
35     99
36     101


Output: 665

Sample input: 1012

Chart of possible bases: 

Base   Value
3      32
4      70
5      132
6      224
7      352
8      522
9      740
10     1012
11     1344
12     1742
13     2212
14     2760
15     3392
16     4114
17     4932
18     5852
19     6880
20     8022
21     9284
22     10672
23     12192
24     13850
25     15652
26     17604
27     19712
28     21982
29     24420
30     27032
31     29824
32     32802
33     35972
34     39340
35     42912
36     46694


Output: 444278

Sample input: HELLOworld

Chart of possible bases

Base   Value
33     809608041709942
34     1058326557132355
35     1372783151310948
36     1767707668033969


Output: 5008425418187214

An input of 0 would be read as 0 in all bases between 2 and 36 inclusive. There is no such thing as base 1.



This is code golf. Standard rules apply. Shortest code in bytes wins.
Python 3, 72 71 69 bytes
Thanks to FryAmTheEggman for saving a byte!
Thanks to DSM for saving 2 bytes!
N=x=0
y=input()
while N&lt;36:
 N+=1
 try:x+=int(y,N)
 except:0
print(x)