310817: CF1893C. Freedom of Choice

C. Freedom of Choicetime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard output

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.

Input

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 $10^5$.

Output

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

ExampleInput

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

Output

1
139
0
1
1
0
0

Note

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 $1$.

题目大意：
定义一个多重集的“反美”为其包含的元素数量与该多重集的长度的相同数的个数。给你m个多重集，每个多重集包含n_i个不同的元素，具体为c_{i, 1}个a_{i,1}，c_{i, 2}个a_{i,2}等，直到c_{i, n_i}个a_{i, n_i}。还给你l_1, l_2, ..., l_m和r_1, r_2, ..., r_m，要求从每个多重集中选择v_i个元素（l_i ≤ v_i ≤ r_i）加入到多重集X中，目标是使X的“反美”最小。

输入输出数据格式：
输入：
第一行包含一个整数t（1 ≤ t ≤ 10^4），表示测试用例的数量。
每个测试用例的第一行包含一个整数m（1 ≤ m ≤ 10^5），表示给定的多重集的数量。
接下来，对于每个i从1到m，输入一个数据块，包含三行：
第一行包含三个整数n_i, l_i, r_i（1 ≤ n_i ≤ 10^5, 1 ≤ l_i ≤ r_i ≤ c_{i, 1} + ... + c_{i, n_i} ≤ 10^17），分别表示第i个多重集中不同元素的数量以及在X中从第i个多重集添加元素的数量限制。
第二行包含n_i个整数a_{i, 1}, ..., a_{i, n_i}（1 ≤ a_{i, 1} < ... < a_{i, n_i} ≤ 10^17），表示第i个多重集中的不同元素。
第三行包含n_i个整数c_{i, 1}, ..., c_{i, n_i}（1 ≤ c_{i, j} ≤ 10^12），表示第i个多重集中元素的副本数。

输出：
对于每个测试用例，输出可以实现的X的最小“反美”。题目大意： 定义一个多重集的“反美”为其包含的元素数量与该多重集的长度的相同数的个数。给你m个多重集，每个多重集包含n_i个不同的元素，具体为c_{i, 1}个a_{i,1}，c_{i, 2}个a_{i,2}等，直到c_{i, n_i}个a_{i, n_i}。还给你l_1, l_2, ..., l_m和r_1, r_2, ..., r_m，要求从每个多重集中选择v_i个元素（l_i ≤ v_i ≤ r_i）加入到多重集X中，目标是使X的“反美”最小。 输入输出数据格式： 输入： 第一行包含一个整数t（1 ≤ t ≤ 10^4），表示测试用例的数量。 每个测试用例的第一行包含一个整数m（1 ≤ m ≤ 10^5），表示给定的多重集的数量。 接下来，对于每个i从1到m，输入一个数据块，包含三行： 第一行包含三个整数n_i, l_i, r_i（1 ≤ n_i ≤ 10^5, 1 ≤ l_i ≤ r_i ≤ c_{i, 1} + ... + c_{i, n_i} ≤ 10^17），分别表示第i个多重集中不同元素的数量以及在X中从第i个多重集添加元素的数量限制。 第二行包含n_i个整数a_{i, 1}, ..., a_{i, n_i}（1 ≤ a_{i, 1} < ... < a_{i, n_i} ≤ 10^17），表示第i个多重集中的不同元素。 第三行包含n_i个整数c_{i, 1}, ..., c_{i, n_i}（1 ≤ c_{i, j} ≤ 10^12），表示第i个多重集中元素的副本数。 输出： 对于每个测试用例，输出可以实现的X的最小“反美”。