AtCoder Beginner Contest 128
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Problem Statement
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We have $N$ switches with "on" and "off" state, and $M$ bulbs. The switches are numbered $1$ to $N$, and the bulbs are numbered $1$ to $M$.
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Bulb $i$ is connected to $k_i$ switches: Switch $s_{i1}$, $s_{i2}$, $...$, and $s_{ik_i}$. It is lighted when the number of switches that are "on" among these switches is congruent to $p_i$ modulo $2$.
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How many combinations of "on" and "off" states of the switches light all the bulbs?
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Constraints
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$1 \leq N, M \leq 10$$1 \leq k_i \leq N$$1 \leq s_{ij} \leq N$$s_{ia} \neq s_{ib} (a \neq b)$$p_i$is$0$or$1$.- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N M
k_1 s_{11} s_{12} ... s_{1k_1}
:
k_M s_{M1} s_{M2} ... s_{Mk_M}
p_1 p_2 ... p_M翻译中…
Output
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Print the number of combinations of "on" and "off" states of the switches that light all the bulbs.
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样例
Input #1
2 2
2 1 2
1 2
0 1
Output #1
1
- Bulb $1$ is lighted when there is an even number of switches that are "on" among the following: Switch $1$ and $2$.
- Bulb $2$ is lighted when there is an odd number of switches that are "on" among the following: Switch $2$.
There are four possible combinations of states of (Switch $1$, Switch $2$): (on, on), (on, off), (off, on) and (off, off). Among them, only (on, on) lights all the bulbs, so we should print $1$.
Input #2
2 3
2 1 2
1 1
1 2
0 0 1
Output #2
0
- Bulb $1$ is lighted when there is an even number of switches that are "on" among the following: Switch $1$ and $2$.
- Bulb $2$ is lighted when there is an even number of switches that are "on" among the following: Switch $1$.
- Bulb $3$ is lighted when there is an odd number of switches that are "on" among the following: Switch $2$.
Switch $1$ has to be "off" to light Bulb $2$ and Switch $2$ has to be "on" to light Bulb $3$, but then Bulb $1$ will not be lighted. Thus, there are no combinations of states of the switches that light all the bulbs, so we should print $0$.
Input #3
5 2
3 1 2 5
2 2 3
1 0
Output #3
8
题目信息
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