A function f:{1,2,…,n}→{1,…,m} is multiplication-preserving if f(i)f(j)=f(ij) for all 1≤i≤j≤ij≤n, and injective if f(i)=f(j) only when i=j. For n=9,m=88, the number of injective, multiplication-preserving functions is N. Find the sum of the prime factors of N, including multiplicity. (For example, if N=12, the answer would be 2+2+3=7.)