Problem #69
Trio Interchange
There is a six digit number, which when multiplied with 6, yields another six digit number, with first three digits of original number as the last three digits of the new number, in the same order, and the last three digits of the original number as the first three digits of the new number, in the same order.
Let S be the sum of the digits of that number. Find S!\bmod {1000000007}