CF1284B New Year and Ascent Sequence

A sequence $ a = [a_1, a_2, \ldots, a_l] $ of length $ l $ has an ascent if there exists a pair of indices $ (i, j) $ such that $ 1 \le i < j \le l $ and $ a_i < a_j $ . For example, the sequence $ [0, 2, 0, 2, 0] $ has an ascent because of the pair $ (1, 4) $ , but the sequence $ [4, 3, 3, 3, 1] $ doesn't have an ascent. Let's call a concatenation of sequences $ p $ and $ q $ the sequence that is obtained by writing down sequences $ p $ and $ q $ one right after another without changing the order. For example, the concatenation of the $ [0, 2, 0, 2, 0] $ and $ [4, 3, 3, 3, 1] $ is the sequence $ [0, 2, 0, 2, 0, 4, 3, 3, 3, 1] $ . The concatenation of sequences $ p $ and $ q $ is denoted as $ p+q $ . Gyeonggeun thinks that sequences with ascents bring luck. Therefore, he wants to make many such sequences for the new year. Gyeonggeun has $ n $ sequences $ s_1, s_2, \ldots, s_n $ which may have different lengths. Gyeonggeun will consider all $ n^2 $ pairs of sequences $ s_x $ and $ s_y $ ( $ 1 \le x, y \le n $ ), and will check if its concatenation $ s_x + s_y $ has an ascent. Note that he may select the same sequence twice, and the order of selection matters. Please count the number of pairs ( $ x, y $ ) of sequences $ s_1, s_2, \ldots, s_n $ whose concatenation $ s_x + s_y $ contains an ascent.

The first line contains the number $ n $ ( $ 1 \le n \le 100\,000 $ ) denoting the number of sequences. The next $ n $ lines contain the number $ l_i $ ( $ 1 \le l_i $ ) denoting the length of $ s_i $ , followed by $ l_i $ integers $ s_{i, 1}, s_{i, 2}, \ldots, s_{i, l_i} $ ( $ 0 \le s_{i, j} \le 10^6 $ ) denoting the sequence $ s_i $ . It is guaranteed that the sum of all $ l_i $ does not exceed $ 100\,000 $ .

Print a single integer, the number of pairs of sequences whose concatenation has an ascent.

For the first example, the following $ 9 $ arrays have an ascent: $ [1, 2], [1, 2], [1, 3], [1, 3], [1, 4], [1, 4], [2, 3], [2, 4], [3, 4] $ . Arrays with the same contents are counted as their occurences.