Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana

In this problem, we refer to the digits of a positive integer as the sequence of digits required to write it in base $10$ without leading zeros. For instance, the digits of $N = 2090$ are of course $2$, $0$, $9$ and $0$. Let $N$ be a positive integer. We call a positive integer $M$ an eleven-multiple-anagram of $N$ if and only if (1) the digits of $M$ are a permutation of the digits of $N$, and (2) $M$ is a multiple of $11$. You are required to write a program that given $N$, calculates the number of its eleven-multiple-anagrams. As an example, consider again $N = 2090$. The values that meet the rst condition above are $2009$, $2090$, $2900$, $9002$, $9020$ and $9200$. Among those, only $2090$ and $9020$ satisfy the second condition, so the answer for $N = 2090$ is $2$.

A single line that contains an integer $N (1 \leq N \leq 10^{100})$.

Output a line with an integer representing the number of eleven-multiple-anagrams of $N$. Because this number can be very large, you are required to output the remainder of dividing it by $10^9 + 7$.