CF491B.New York Hotel

Think of New York as a rectangular grid consisting of N vertical avenues numerated from 1 to N and M horizontal streets numerated 1 to M. C friends are staying at C hotels located at some street-avenue crossings. They are going to celebrate birthday of one of them in the one of H restaurants also located at some street-avenue crossings. They also want that the maximum distance covered by one of them while traveling to the restaurant to be minimum possible. Help friends choose optimal restaurant for a celebration.

Suppose that the distance between neighboring crossings are all the same equal to one kilometer.

将纽约视为一个矩形网格，包含 $N$ 条纵向大道（编号从 $1$ 到 $N$）和 $M$ 条横向街道（编号从 $1$ 到 $M$）。$C$ 位朋友住在位于某些街-道交叉口的 $C$ 家酒店中。他们计划在 $H$ 家餐厅（同样位于某些街-道交叉口）中的某一家为其中一位朋友庆祝生日。他们还希望所有人前往该餐厅途中，单人所行距离的最大值尽可能小。请帮助这些朋友选择最优的庆祝餐厅。

假设相邻交叉口之间的距离均相等，为一公里。

The first line contains two integers N и M — size of the city (1 ≤ N, M ≤ 109). In the next line there is a single integer C (1 ≤ C ≤ 105) — the number of hotels friends stayed at. Following C lines contain descriptions of hotels, each consisting of two coordinates x and y (1 ≤ x ≤ N, 1 ≤ y ≤ M). The next line contains an integer H — the number of restaurants (1 ≤ H ≤ 105). Following H lines contain descriptions of restaurants in the same format.

Several restaurants and hotels may be located near the same crossing.

第一行包含两个整数 $N$ 和 $M$ —— 城市的尺寸（$1 \leq N, M \leq 10^9$）。
第二行包含一个整数 $C$（$1 \leq C \leq 10^5$）—— 朋友们入住的酒店数量。
接下来的 $C$ 行描述了这些酒店，每行包含两个坐标 $x$ 和 $y$（$1 \leq x \leq N$, $1 \leq y \leq M$）。
下一行包含一个整数 $H$ —— 餐厅的数量（$1 \leq H \leq 10^5$）。
接下来的 $H$ 行以相同格式描述了这些餐厅。

多个餐厅和酒店可能位于同一个路口附近。

In the first line output the optimal distance. In the next line output index of a restaurant that produces this optimal distance. If there are several possibilities, you are allowed to output any of them.

第一行输出最优距离。
第二行输出产生该最优距离的餐厅索引。若存在多种可能，输出任意一个即可。