Cloud Retainer's Game

Cloud Retainer, the builder of the Dwelling in the clouds above Qingyun Peak, is very interested in mechanics. The Lantern Rite Festival in Liyue is more than a month away, but she has already started designing a gaming event for it.

Cloud Retainer and the Traveler

The game is mainly about releasing pinballs to score as high as possible. It is played on a two-dimensional plane with two horizontal lines $y = 0$ and $y = H$. Between the two lines are $n$ tiny wooden boards and $m$ coins. Both are single points. The $i$-th wooden board is at $(x_i, y_i)$, and the $i$-th coin is at $(x'_i, y'_i)$.

The player releases a pinball from $(10^{-9}, 10^{-9})$. Let $\overrightarrow{v} = (v_x, v_y)$ be the velocity of the ball. If the ball is at $(x, y)$, it moves to $(x + v_x\epsilon, y + v_y\epsilon)$ after $\epsilon$ seconds. Initially $\overrightarrow{v} = (1, 1)$.

When the ball hits a wooden board or one of the two horizontal lines, $v_y$ is negated and $v_x$ stays the same. When the ball hits a coin, the score goes up by 1 and the velocity stays the same.

Before the release, the player may remove any number of wooden boards, including none. Cloud Retainer wants to estimate the difficulty of the game. Find the maximum score the player can get after $10^{10^{10^{10^{10}}}}$ seconds under the best strategy.

The first line contains an integer $T$, the number of test cases. Each test case has the following format.

The first line contains $H$ ($2 \le H \le 10^9$).

The second line contains $n$ ($1 \le n \le 10^5$), the number of wooden boards. The next $n$ lines each contain $x_i$ and $y_i$ ($1 \le x_i \le 10^9$, $1 \le y_i < H$), the location of the $i$-th wooden board.

The next line contains $m$ ($1 \le m \le 10^5$), the number of coins. The next $m$ lines each contain $x'_i$ and $y'_i$ ($1 \le x'_i \le 10^9$, $1 \le y'_i < H$), the location of the $i$-th coin.

All $n + m$ points in a test case are distinct. The sums of $n$ and of $m$ over all test cases do not exceed $5 \times 10^5$.

For each test case, print one line with the maximum score the player can get after removing some wooden boards, or none.

The figure below shows two test cases. Solid diamonds are remaining wooden boards, hollow diamonds are removed wooden boards, and round dots are coins.

Test case 1	Test case 2