AT_abc402_c [ABC402C] Dislike Foods

The AtCoder Restaurant uses $ N $ types of ingredients numbered from $ 1 $ to $ N $ . The restaurant offers $ M $ dishes numbered from $ 1 $ to $ M $ . Dish $ i $ uses $ K_i $ types of ingredients, namely $ A_{i,1}, A_{i,2}, \ldots, A_{i,K_i} $ . Snuke currently dislikes all $ N $ ingredients. He cannot eat any dish that uses one or more ingredients he dislikes, and he can eat a dish that uses none of the disliked ingredients. Over the next $ N $ days, he will overcome his dislikes one ingredient per day. On day $ i $ , he overcomes ingredient $ B_i $ , and from then on he no longer dislikes it. For each $ i=1,2,\ldots,N $ , find: - the number of dishes at the AtCoder Restaurant that he can eat immediately after overcoming ingredient $ B_i $ on day $ i $ .

The input is given from Standard Input in the following format: > $ N $ $ M $ $ K_1 $ $ A_{1,1} $ $ A_{1,2} $ $ \ldots $ $ A_{1,K_1} $ $ K_2 $ $ A_{2,1} $ $ A_{2,2} $ $ \ldots $ $ A_{2,K_2} $ $ \vdots $ $ K_M $ $ A_{M,1} $ $ A_{M,2} $ $ \ldots $ $ A_{M,K_M} $ $ B_1 $ $ B_2 $ $ \ldots $ $ B_N $

Print $ N $ lines. The $ k $ -th line should contain the answer for $ i=k $ .

### Sample Explanation 1 Snuke overcomes his disliked ingredients as follows: - Day $ 1 $ : He overcomes ingredient $ 1 $ . At this time, every dish still uses a disliked ingredient, so print $ 0 $ . - Day $ 2 $ : He overcomes ingredient $ 3 $ . Dish $ 4 $ no longer uses any disliked ingredient and becomes edible; all other dishes still use disliked ingredients, so print $ 1 $ . - Day $ 3 $ : He overcomes ingredient $ 2 $ . Dish $ 1 $ no longer uses any disliked ingredient and becomes edible; all dishes except $ 1 $ and $ 4 $ still use disliked ingredients, so print $ 2 $ . - Day $ 4 $ : He overcomes ingredient $ 5 $ . Dish $ 3 $ no longer uses any disliked ingredient and becomes edible; all dishes except $ 1 $ , $ 3 $ , and $ 4 $ still use disliked ingredients, so print $ 3 $ . - Day $ 5 $ : He overcomes ingredient $ 4 $ . Dish $ 2 $ no longer uses any disliked ingredient and becomes edible; now all dishes have no disliked ingredients, so print $ 4 $ . ### Constraints - $ 1 \leq N \leq 3 \times 10^{5} $ - $ 1 \leq M \leq 3 \times 10^{5} $ - $ 1 \leq K_i \leq N $ $ (1 \leq i \leq M) $ - The sum of $ K_i $ is at most $ 3 \times 10^{5} $ . - $ 1 \leq A_{i,j} \leq N $ $ (1 \leq i \leq M, 1 \leq j \leq K_i) $ - $ A_{i,j} \neq A_{i,k} $ $ (1 \leq i \leq M, j \neq k) $ - $ 1 \leq B_i \leq N $ $ (1 \leq i \leq N) $ - $ B_i \neq B_j $ $ (i \neq j ) $ - All input values are integers.