###Introduction
Let's observe the following sequence (non-negative integers):
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ...
For example, let's take the first three numbers. These are 0, 1, 2. The numbers used in this sequence can be ordered in six different ways:
012 120
021 201
102 210
So, let's say that F(3) = 6. Another example is F(12). This contains the numbers:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Or the concatenated version:
01234567891011
To find the number of ways to rearrange this, we first need to look at the length of this string. The length of this string is 14. So we compute 14!. However, for example the ones can exchange places without disrupting the final string. There are 2 zeroes, so there are 2! ways to exhange the zeroes without disrupting the order. There are also 4 ones, so there are 4! ways to switch the ones. We divide the total by these two numbers:
This has 14! / (4! × 2!) = 1816214400 ways to arrange the string 01234567891011. So we can conclude that F(12) = 1816214400.
###The task
Given N, output F(N). For the ones who don't need the introduction. To compute F(N), we first concatenate the first N non-negative integers (e.g. for N = 12, the concatenated string would be 01234567891011) and calculate the number of ways to arrange this string.
###Test cases
Input: Output:
0 1
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800
11 119750400
12 1816214400
13 43589145600
14 1111523212800
15 30169915776000
###Note
Computing the answer must be computed within a time limit of 10 seconds, brute-forcing is disallowed. Languages using 32 bit integers must handle the test-cases up to 11, but must theoretically work for all of them (when given unlimited memory).
This is code-golf, so the submission with the least amount of bytes wins!
