B'You are given an integer m as a product of integers a1, xe2 x80 x89a2, xe2 x80 x89... an . Your task is to find the number of distinct decompositions of number m into the product of n ordered positive integers. Decomposition into n products, given in the input, must also be considered in the answer. As the answer can be very large, print it modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). The first line contains positive integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89500). The second line contains space-separated integers a1, xe2 x80 x89a2, xe2 x80 x89..., xe2 x80 x89an (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89109). In a single line print a single number k -- the number of distinct decompositions of number m into n ordered multipliers modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). In the second sample, the get a decomposition of number 2, you need any one number out of three to equal 2, and the rest to equal 1. In the third sample, the possible ways of decomposing into ordered multipliers are [7,5], [5,7], [1,35], [35,1]. A decomposition of positive integer m into n ordered multipliers is a cortege of positive integers b xe2 x80 x89= xe2 x80 x89{b1, xe2 x80 x89b2, xe2 x80 x89... bn} such that . Two decompositions b and c are considered different, if there exists index i such that bi xe2 x80 x89 xe2 x89 xa0 xe2 x80 x89ci.'...