Do you remember the tower defense game titled "Bomb Attack"? This game has a sequel, and the power of the bombs has been greatly increased.

The game map is a 2D plane. JYY's base is located below the $x$-axis, while all enemies are currently located above the $x$-axis.

In JYY's base, there are $T$ laser towers and $S$ energy emitters. The $i$-th defensive tower $T_i$ has coordinates $(tx_i, ty_i)$, and the $i$-th energy emitter $S_i$ has coordinates $(sx_i, sy_i)$.

There are $D$ enemies on the map, and the $i$-th enemy $D_i$ has coordinates $(dx_i, dy_i)$.

Two laser towers can be connected to form an energy wall. If the energy emitted from an emitter toward an enemy passes through an energy wall, it receives a massive boost, becoming a "super ray" that instantly eliminates the enemy.

JYY wants to know how many ways he can fire a super ray.

Specifically, an attack plan that can fire a super ray is a set of four points $\{T_i, T_j, S_k, D_l\}$ satisfying $1 \le i < j \le T$, $1 \le k \le S$, and $1 \le l \le D$, such that the line segment $T_i T_j$ and the line segment $S_k D_l$ intersect.

The game settings guarantee that among these $T + D + S$ points, there are no coincident points and no three points are collinear.

Input

The first line contains a positive integer $D$. The next $D$ lines each contain two integers $dx_i, dy_i$ ($dy_i > 0$), representing the coordinates of an enemy. The next line contains an integer $S$. The next $S$ lines each contain two integers $sx_i, sy_i$ ($sy_i < 0$), representing the coordinates of an energy emitter. The next line contains an integer $T$. The next $T$ lines each contain two integers $tx_i, ty_i$ ($ty_i < 0$), representing the coordinates of a laser tower.

Output

Output a single integer representing the number of attack plans that can fire a super ray.

Examples

Input 1

3
1 12
10 30
30 10
1
10 -10
4
2 -11
9 -1
11 -1
15 -14

Output 1

7

Constraints

• For 20% of the data, $D, S, T \le 30$.
• For 50% of the data, $D, S, T \le 150$.
• For 100% of the data, $1 \le D, S, T \le 800$, and the absolute values of all coordinates do not exceed $10^9$.