Statement

Kida decided to test you knowledge again. You are given a list V, of N integers. Kida asks you to count the number of interesting subsets that satisfy the following condition: for any two numbers V_x and V_y in the subset, V_x appears in the subset the same number of times as V_y. Two subsets are considered different if there is at least one value i such that V_i is in one subset but not in the other. Note that two different subsets might contain the exactly same numbers. Since this number can be very large, you need to count it modulo 10^9+7.