CF1320C.World of Darkraft: Battle for Azathoth

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 $a_i \gt x_k$ and $b_j \gt y_k$. 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.

罗玛正在玩他最喜爱的游戏《暗黑纪元》（World of Darkraft）的新资料片。他创建了一个新角色，准备开始首次刷怪。

罗玛必须恰好从 $n$ 种不同的武器中选择一种，且恰好从 $m$ 种不同的护甲套装中选择一套。武器 $i$ 的攻击力加成为 $a_i$，售价为 $ca_i$ 金币；护甲套装 $j$ 的防御力加成为 $b_j$，售价为 $cb_j$ 金币。

选定装备后，罗玛即可挑战若干怪物。共有 $p$ 只怪物可供挑战。怪物 $k$ 的防御力为 $x_k$、攻击力为 $y_k$，击败后可获得 $z_k$ 金币。罗玛能够击败怪物 $k$，当且仅当他所选武器的攻击力加成严格大于该怪物的防御力，且所选护甲套装的防御力加成严格大于该怪物的攻击力。即：使用武器 $i$ 和护甲套装 $j$ 能击败怪物 $k$ 的充要条件是 $a_i \gt x_k$ 且 $b_j \gt y_k$。击败怪物后，罗玛将获得其全部金币。在整个刷怪过程中，罗玛可以击败任意数量的怪物（只要满足条件），但怪物不会刷新，因此每只怪物最多只能被击败一次。

得益于罗玛巨额的充值，我们可以假定他拥有无限的游戏内货币，能够负担得起任意武器和护甲套装。然而，他仍希望最大化本次刷怪的收益。收益定义为：所有被击败怪物所获金币总和减去所购装备的总花费。注意：即使罗玛无法通过击败怪物获得足够金币来覆盖装备开销，他也必须购买一件武器和一套护甲。

请帮助罗玛计算本次刷怪所能获得的最大收益。

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 $k$.

第一行包含三个整数 $n$、$m$ 和 $p$（$1 \leq n, m, p \leq 2 \cdot 10^5$），分别表示可用武器数量、可用护甲套装数量以及怪物数量。

接下来的 $n$ 行描述可用武器。其中第 $i$ 行包含两个整数 $a_i$ 和 $ca_i$（$1 \leq a_i \leq 10^6$，$1 \leq ca_i \leq 10^9$），分别表示第 $i$ 件武器的攻击力加成和价格。

接下来的 $m$ 行描述可用护甲套装。其中第 $j$ 行包含两个整数 $b_j$ 和 $cb_j$（$1 \leq b_j \leq 10^6$，$1 \leq cb_j \leq 10^9$），分别表示第 $j$ 套护甲的防御力加成和价格。

接下来的 $p$ 行描述怪物。其中第 $k$ 行包含三个整数 $x_k$、$y_k$、$z_k$（$1 \leq x_k, y_k \leq 10^6$，$1 \leq z_k \leq 10^3$），分别表示第 $k$ 个怪物的防御力、攻击力以及金币数量。

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

输出一个整数——该研磨操作所能获得的最大利润。