Light switches

题意翻译

有 $N$ 个灯泡，标号为 $1$ 至 $N$。 有 $S$ 个开关，按下第 $i$ 个开关会改变 $C_i$ 个灯泡的开关状态。每个开关影响的灯泡序号是给定的，且不变。 有 $D$ 次询问，每次给定开着的灯泡的序号，其余灯泡都是关闭的，并询问令所有灯泡都关闭的最少操作次数。如果没有合法方案，输出 `-1`。

题目描述

Nikola owns a large warehouse which is illuminated by $ N $ light bulbs, numbered $ 1 $ to $ N $ . At the exit of the warehouse, there are $ S $ light switches, numbered $ 1 $ to $ S $ . Each switch swaps the on/off state for some light bulbs, so if a light bulb is off, flipping the switch turns it on, and if the light bulb is on, flipping the switch turns it off. At the end of the day, Nikola wants to turn all the lights off. To achieve this, he will flip some of the light switches at the exit of the warehouse, but since Nikola is lazy, he wants to flip the \_minimum\_ number of switches required to turn all the lights off. Since Nikola was not able to calculate the minimum number of switches, he asked you to help him. During a period of $ D $ days, Nikola noted which light bulbs were off and which were on at the end of each day. He wants you to tell him the minimum number of switches he needed to flip to turn all the lights off for each of the $ D $ days or tell him that it's impossible.

输入输出格式

输入格式

First line contains three integers, $ N $ , $ S $ and $ D $ ( $ 1 \leq N \leq 10^3 $ , $ 1 \leq S \leq 30 $ , $ 1 \leq D \leq 10^3 $ ) – representing number of light bulbs, the number of light switches, and the number of days respectively. The next $ S $ lines contain the description of each light switch as follows: The first number in the line, $ C_i $ ( $ 1 \leq C_i \leq N $ ), represents the number of light bulbs for which the on/off state is swapped by light switch $ i $ , the next $ C_i $ numbers (sorted in increasing order) represent the indices of those light bulbs. The next $ D $ lines contain the description of light bulbs for each day as follows: The first number in the line, $ T_i $ ( $ 1 \leq T_i \leq N $ ), represents the number of light bulbs which are on at the end of day $ i $ , the next $ T_i $ numbers (sorted in increasing order) represent the indices of those light bulbs.

输出格式

Print $ D $ lines, one for each day. In the $ i^{th} $ line, print the minimum number of switches that need to be flipped on day $ i $ , or $ -1 $ if it's impossible to turn all the lights off.

输入输出样例

输入样例 #1

4 3 4
2 1 2
2 2 3
1 2
1 1
2 1 3
3 1 2 3
3 1 2 4

输出样例 #1

2
2
3
-1