Codeforces Round 908 (Div. 1) |
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Finished |

brute force

greedy

implementation

*2000

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C. Freedom of Choice

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputLet'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.

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.

Example

Input

733 5 610 11 123 3 11 1 31242 4 412 131 517 1000 10061000 1001 1002 1003 1004 1005 1006147 145 143 143 143 143 14212 48 5048 5025 2521 1 1111 1 12111 1 11221 1 1112 1 11 21 124 8 1011 12 13 143 3 3 32 3 411 122 2

Output

1 139 0 1 1 0 0

Note

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 $$$1$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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