Problem 250 Published on Saturday, 13th June 2009, 05:00 am; Solved by 2404; Difficulty rating: 55%

Find the number of non-empty subsets of {1^{1}, 2^{2}, 3^{3},..., 250250^{250250}}, the sum of whose elements is divisible by 250. Enter the rightmost 16 digits as your answer.