World of Darkraft: Battle for Azathoth

### 题目描述 给定 $n$ 件武器、$m$ 件防具和 $p$ 只怪物 $(1 \le n,m,p \le 2 \times 10^5)$，武器 $i$ 提供攻击力 $a_i$，价格为 $ca_i$ 枚金币 $(1 \le a_i \le 10^6,1 \le ca_i \le 10^9)$；防具 $j$ 提供防御力 $b_j$，价格为 $cb_j$ 枚金币 $(1 \le b_j \le 10^6,1 \le cb_j \le 10^9)$；怪物 $k$ 的防御力为 $x_k$，攻击力为 $y_k$，击杀会掉落 $z_k$ 枚金币 $(1 \le x_k,y_k \le 10^6,1 \le z_k \le 10^3)$。 如果购买武器的攻击力**严格大于**怪物 $k$ 的防御力，且购买防具的防御力**严格大于**怪物 $k$ 的攻击力，那么可以击杀该怪物，并获得其掉落金币。武器和防具不会被消耗，但每只怪物只能被击杀一次。 现在规定能且只能购买一件武器和一件防具，求出收益（掉落金币的总数减去购买武器和防具的花费总和）的最大值。 ### 输入格式 第一行输入三个整数 $n$，$m$ 和 $p$，分别表示武器件数、防具件数和怪物总数。 接下来 $n$ 行，每行有两个整数 $a_i$ 和 $ca_i$，分别表示第 $i$ 件武器的攻击力和价格。 接下来 $m$ 行，每行有两个整数 $b_j$ 和 $cb_j$，分别表示第 $j$ 件防具的防御力和价格。 接下来 $p$ 行，每行有三个整数 $x_k$，$y_k$ 和 $z_k$，分别表示第 $k$ 只怪物的防御力、攻击力和击杀掉落金币。 ### 输出格式 输出共一行，只有一个整数，表示收益的最大值。

Roma is playing a new expansion for his favorite game World of Darkraft. He made a new character and is going for his first grind. Roma has a choice to buy exactly one of $ n $ different weapons and exactly one of $ m $ different armor sets. Weapon $ i $ has attack modifier $ a_i $ and is worth $ ca_i $ coins, and armor set $ j $ has defense modifier $ b_j $ and is worth $ cb_j $ coins. After choosing his equipment Roma can proceed to defeat some monsters. There are $ p $ monsters he can try to defeat. Monster $ k $ has defense $ x_k $ , attack $ y_k $ and possesses $ z_k $ coins. Roma can defeat a monster if his weapon's attack modifier is larger than the monster's defense, and his armor set's defense modifier is larger than the monster's attack. That is, a monster $ k $ can be defeated with a weapon $ i $ and an armor set $ j $ if $ a_i > x_k $ and $ b_j > y_k $ . After defeating the monster, Roma takes all the coins from them. During the grind, Roma can defeat as many monsters as he likes. Monsters do not respawn, thus each monster can be defeated at most one. Thanks to Roma's excessive donations, we can assume that he has an infinite amount of in-game currency and can afford any of the weapons and armor sets. Still, he wants to maximize the profit of the grind. The profit is defined as the total coins obtained from all defeated monsters minus the cost of his equipment. Note that Roma must purchase a weapon and an armor set even if he can not cover their cost with obtained coins. Help Roma find the maximum profit of the grind.

The first line contains three integers $ n $ , $ m $ , and $ p $ ( $ 1 \leq n, m, p \leq 2 \cdot 10^5 $ ) — the number of available weapons, armor sets and monsters respectively. The following $ n $ lines describe available weapons. The $ i $ -th of these lines contains two integers $ a_i $ and $ ca_i $ ( $ 1 \leq a_i \leq 10^6 $ , $ 1 \leq ca_i \leq 10^9 $ ) — the attack modifier and the cost of the weapon $ i $ . The following $ m $ lines describe available armor sets. The $ j $ -th of these lines contains two integers $ b_j $ and $ cb_j $ ( $ 1 \leq b_j \leq 10^6 $ , $ 1 \leq cb_j \leq 10^9 $ ) — the defense modifier and the cost of the armor set $ j $ . The following $ p $ lines describe monsters. The $ k $ -th of these lines contains three integers $ x_k, y_k, z_k $ ( $ 1 \leq x_k, y_k \leq 10^6 $ , $ 1 \leq z_k \leq 10^3 $ ) — defense, attack and the number of coins of the monster $ k $ .

Print a single integer — the maximum profit of the grind.

2 3 3
2 3
4 7
2 4
3 2
5 11
1 2 4
2 1 6
3 4 6

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