Freedom of Choice

注：下文中的 multiset 均为可重集。 我们定义一个大小为 $len$ 的 multiset 的不优美度为数 $len$ 在这个 multiset 里的出现次数。 给你 $m$ 个 multiset，第 $i$ 个 multiset 包含 $n_i$ 个不同的元素，具体的：这个 multiset 中含有 $c_{i,1}$ 个 $a_{i,1}$，$c_{i,2}$ 个 $a_{i,2}$，$\dots$，$c_{i,n_i}$ 个 $a_{i,n_i}$。保证 $ a_{i, 1} < a_{i, 2} < \ldots < a_{i, n_i} $。同时给你 $ l_1, l_2, \ldots, l_m $ 和 $ r_1, r_2, \ldots, r_m $，其中 $ 1 \le l_i \le r_i \le c_{i, 1} + \ldots + c_{i, n_i} $ 。 我们按照如下操作创建一个 multiset X，最初 X 为空。然后，对于 $1$ 到 $m$ 的每一个数 $i$，执行下面的操作： 1.选择一个数 $v_i$ 使得 $ l_i \le v_i \le r_i $ 2.从第 $i$ 个 multiset 里选择任意 $v_i$ 个数并把它们加入 X。 你的任务是选择 $ v_1, \ldots, v_m $ ，使得 mutiset X 的不优美度最小。 多测，$ 1 \le t \le 10^4 $ , $ 1 \le m \le 10^5 $，$ 1 \le n_i \le 10^5, 1 \le l_i \le r_i \le c_{i, 1} + \ldots + c_{i, n_i} \le 10^{17} $，$ 1 \le a_{i, 1} < \ldots < a_{i, n_i} \le 10^{17} $， $ 1 \le c_{i, j} \le 10^{12} $ ，$m$ 的总和以及所有数据里的 $n_i$ 的总和不超过 $10^5$。 翻译来自@[brimosta](https://www.luogu.com.cn/user/247193)

Let's define the anti-beauty of a multiset $ \{b_1, b_2, \ldots, b_{len}\} $ as the number of occurrences of the number $ len $ in the multiset. You are given $ m $ multisets, where the $ i $ -th multiset contains $ n_i $ distinct elements, specifically: $ c_{i, 1} $ copies of the number $ a_{i,1} $ , $ c_{i, 2} $ copies of the number $ a_{i,2}, \ldots, c_{i, n_i} $ copies of the number $ a_{i, n_i} $ . It is guaranteed that $ a_{i, 1} < a_{i, 2} < \ldots < a_{i, n_i} $ . You are also given numbers $ l_1, l_2, \ldots, l_m $ and $ r_1, r_2, \ldots, r_m $ such that $ 1 \le l_i \le r_i \le c_{i, 1} + \ldots + c_{i, n_i} $ . Let's create a multiset $ X $ , initially empty. Then, for each $ i $ from $ 1 $ to $ m $ , you must perform the following action exactly once: 1. Choose some $ v_i $ such that $ l_i \le v_i \le r_i $ 2. Choose any $ v_i $ numbers from the $ i $ -th multiset and add them to the multiset $ X $ . You need to choose $ v_1, \ldots, v_m $ and the added numbers in such a way that the resulting multiset $ X $ has the minimum possible anti-beauty.

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ m $ ( $ 1 \le m \le 10^5 $ ) — the number of given multisets. Then, for each $ i $ from $ 1 $ to $ m $ , a data block consisting of three lines is entered. The first line of each block contains three integers $ n_i, l_i, r_i $ ( $ 1 \le n_i \le 10^5, 1 \le l_i \le r_i \le c_{i, 1} + \ldots + c_{i, n_i} \le 10^{17} $ ) — the number of distinct numbers in the $ i $ -th multiset and the limits on the number of elements to be added to $ X $ from the $ i $ -th multiset. The second line of the block contains $ n_i $ integers $ a_{i, 1}, \ldots, a_{i, n_i} $ ( $ 1 \le a_{i, 1} < \ldots < a_{i, n_i} \le 10^{17} $ ) — the distinct elements of the $ i $ -th multiset. The third line of the block contains $ n_i $ integers $ c_{i, 1}, \ldots, c_{i, n_i} $ ( $ 1 \le c_{i, j} \le 10^{12} $ ) — the number of copies of the elements in the $ i $ -th multiset. It is guaranteed that the sum of the values of $ m $ for all test cases does not exceed $ 10^5 $ , and also the sum of $ n_i $ for all blocks of all test cases does not exceed $ 10^5 $ .

For each test case, output the minimum possible anti-beauty of the multiset $ X $ that you can achieve.

7
3
3 5 6
10 11 12
3 3 1
1 1 3
12
4
2 4 4
12 13
1 5
1
7 1000 1006
1000 1001 1002 1003 1004 1005 1006
147 145 143 143 143 143 142
1
2 48 50
48 50
25 25
2
1 1 1
1
1
1 1 1
2
1
1
1 1 1
1
2
2
1 1 1
1
1
2 1 1
1 2
1 1
2
4 8 10
11 12 13 14
3 3 3 3
2 3 4
11 12
2 2

1
139
0
1
1
0
0

In the first test case, the multisets have the following form: 1. $ \{10, 10, 10, 11, 11, 11, 12\} $ . From this multiset, you need to select between $ 5 $ and $ 6 $ numbers. 2. $ \{12, 12, 12, 12\} $ . From this multiset, you need to select between $ 1 $ and $ 3 $ numbers. 3. $ \{12, 13, 13, 13, 13, 13\} $ . From this multiset, you need to select $ 4 $ numbers. You can select the elements $ \{10, 11, 11, 11, 12\} $ from the first multiset, $ \{12\} $ from the second multiset, and $ \{13, 13, 13, 13\} $ from the third multiset. Thus, $ X = \{10, 11, 11, 11, 12, 12, 13, 13, 13, 13\} $ . The size of $ X $ is $ 10 $ , the number $ 10 $ appears exactly $ 1 $ time in $ X $ , so the anti-beauty of $ X $ is $ 1 $ . It can be shown that it is not possible to achieve an anti-beauty less than $ 1 $ .