Anagrams divisible by 11

A natural number can be written as a sequence of digits, and a sequence of digits can be read back as a natural number. A leading zero is not allowed. For example, $N = 2090$ gives the sequence $\{2, 0, 9, 0\}$, while the sequence $\{0, 0, 1, 0\}$ represents no natural number.

An anagram of a sequence keeps the same elements and only changes their order. Anagrams of a natural number are defined the same way. The anagrams of $N = 2090$ are 2009, 2090, 2900, 9002, 9020, 9200.

Given a natural number $N$, write a program that counts how many anagrams of $N$ are multiples of 11. For $N = 2090$, only 2090 and 9020 are multiples of 11, so the answer is 2.

The first line contains a natural number $N$ with no leading zero. ($1 \le N \le 10^{100}$)

Print how many anagrams of $N$ are multiples of 11. The answer can be very large, so print it modulo $10^9 + 7$.