# Problem 520: Simbers

![graphic](img520.gif)

We define a simber to be a positive integer in which any odd digit, if
present, occurs an odd number of times, and any even digit, if present,
occurs an even number of times. For example, 141221242 is a 9-digit
simber because it has three 1's, four 2's and two 4's. Let Q(n) be the
count of all simbers with at most n digits. You are given Q(7) = 287975
and Q(100) mod 1 000 000 123 = 123864868. Find (∑1≤u≤39 Q(2u)) mod 1 000
000 123.