Kia and Kio spent the summer at the port of Mehragan, where (n) lighthouses stand on the cliffs facing the dark sea. The lighthouses of Mehragan do not give light. Every night a number is written in fire on each of them, and the sailors read their way from those numbers. The law of the lighthouses is this: if a lighthouse shows (x) tonight, then tomorrow night it shows the sum of the squares of the decimal digits of (x). For example, a lighthouse showing (23) will show (2^2+3^2=13) tomorrow, then (1^2+3^2=10), and then (1). On night (0) of the season, lighthouse (i) shows the number (a_i). From that night on, the law is applied once every night, forever. Kio calls two lighthouses (i) and (j) in tune if there exists a night after which, forever , both of them show exactly the same number on every single night. Kia asks: how many pairs ((i, j)) with (i \lt j) are in tune? Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 1000)). The description of the test cases follows. Each test case consists of two lines. The first line of each test case contains a single integer (n) ((1 \le n \le 1000)) — the number of lighthouses. The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le 10^9)) — the number shown by each lighthouse on night (0). It is guaranteed that the sum of (n) over all test cases does not exceed (1000). For each test case, print a single integer — the number of pairs ((i, j)) with (i \lt j) such that lighthouses (i) and (j) are in tune. In the first test case: Lighthouse (1) starts at (7): (7 \to 49 \to 97 \to 130 \to 10 \to 1), and it stays at (1) forever. Lighthouses (2) and (4) both start at (4), so they show the same number on every night. Lighthouse (3) starts at (16) and lighthouse (5) starts at (2); each of them