CF1893C.Freedom of Choice

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

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:

Choose some $v_i$ such that $l_i \le v_i \le r_i$
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.

输入格式

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 $10^5$ .

输出格式

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

输入输出样例

输入#1

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

输出#1

说明/提示

In the first test case, the multisets have the following form:

$\{10, 10, 10, 11, 11, 11, 12\}$ . From this multiset, you need to select between $5$ and $6$ numbers.
$\{12, 12, 12, 12\}$ . From this multiset, you need to select between $1$ and $3$ numbers.
$\{12, 13, 13, 13, 13, 13\}$ . 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 $1$ .

首页