B'You like the card board game "Set". Each card contains k features, each of which is equal to a value from the set {0, 1, 2 } . The deck contains all possible variants of cards, that is, there are 3^k different cards in total. A feature for three cards is called good if it is the same for these cards or pairwise distinct. Three cards are called a set if all k features are good for them. For example, the cards (0, 0, 0) , (0, 2, 1) , and (0, 1, 2) form a set, but the cards (0, 2, 2) , (2, 1, 2) , and (1, 2, 0) do not, as, for example, the last feature is not good. A group of five cards is called a meta-set, if there is strictly more than one set among them. How many meta-sets there are among given n distinct cards? The first line of the input contains two integers n and k ( 1 <= n <= 10^3 , 1 <= k <= 20 ) -- the number of cards on a table and the number of card features. The description of the cards follows in the next n lines. Each line describing a card contains k integers c_{i, 1}, c_{i, 2}, ldots, c_{i, k} ( 0 <= c_{i, j} <= 2 ) -- card features. It is guaranteed that all cards are distinct. Output one integer -- the number of meta-sets. Let 's draw the cards indicating the first four features. The first feature will indicate the number of objects on a card: 1 , 2 , 3 . The second one is the color: red, green, purple. The third is the shape: oval, diamond, squiggle. The fourth is filling: open, striped, solid. You can see the first three tests below. For the first two tests, the meta-sets are highlighted. In the first test, the only meta-set is the five cards (0000, 0001, 0002, 0010, 0020) . The sets in it are the triples (0000, 0001, 0002) and (0000, 0010, 0020) . Also, a set is the triple (0100, 1000, 2200) which does not belong to any meta-set. In the second test, the following groups of fiv'...