AT_arc227_d.Median of Binary Strings

You are given length-$M$ strings $S_1,S_2,\ldots,S_N$ consisting of 0 and 1.

Initially, $S_1,S_2,\ldots,S_N$ are written on the blackboard.

You can perform the following operation zero or more times.

• Choose three strings from those written on the blackboard, allowing the same string to be chosen multiple times, and call them $A,B,C$. Newly write on the blackboard a string $D$ of length $M$ satisfying the following condition:
  • For each $i=1,2,\ldots,M$, letting $A_i,B_i,C_i,D_i$ denote the $i$-th characters of $A,B,C,D$, respectively, $D_i$ is equal to at least two of $A_i,B_i,C_i$.

You are given $Q$ strings $T_1,T_2,\ldots,T_Q$. For each $i=1,2,\ldots,Q$, determine whether it is possible to make $T_i$ be written on the blackboard by performing operations starting from the initial state.

给你 $N$ 个长度为 $M$ 的字符串 $S_1, S_2, \ldots, S_N$，每个字符串仅由字符 0 和 1 构成。

初始时，黑板上写有字符串 $S_1, S_2, \ldots, S_N$。

你可以执行以下操作零次或多次：

• 从黑板上已有的字符串中任选三个（允许重复选取同一字符串），记为 $A, B, C$；然后在黑板上新写出一个长度为 $M$ 的字符串 $D$，满足如下条件：
  • 对每个 $i = 1, 2, \ldots, M$，设 $A_i, B_i, C_i, D_i$ 分别为 $A, B, C, D$ 的第 $i$ 个字符，则 $D_i$ 等于 $A_i, B_i, C_i$ 中至少两个的值。

再给你 $Q$ 个字符串 $T_1, T_2, \ldots, T_Q$。对每个 $i = 1, 2, \ldots, Q$，判断是否能从初始状态出发、通过若干次上述操作，使得 $T_i$ 出现在黑板上。

The input is given from Standard Input in the following format:

$N$ $M$ $Q$
$S_1$
$S_2$
$\vdots$
$S_N$
$T_1$
$T_2$
$\vdots$
$T_Q$

输入从标准输入中按以下格式给出：

$N$ $M$ $Q$
$S_1$
$S_2$
$\vdots$
$S_N$
$T_1$
$T_2$
$\vdots$
$T_Q$

Output $Q$ lines. The $i$-th line should contain Yes if $T_i$ can be made to be written on the blackboard, and No otherwise.

输出 $Q$ 行。第 $i$ 行应包含 Yes（如果 $T_i$ 可以被写在黑板上），否则为 No。

Sample 1 Explanation:
$T_1$ is written on the blackboard from the beginning.

$T_2$ is 001. If we perform the operation choosing the three strings 000, 011, 101, we can newly write 001 on the blackboard.

Sample 2 Explanation:
The strings initially written on the blackboard are both 0, and the string newly written by the operation is also 0. Therefore, it is impossible to make 1 be written on the blackboard.

Constraints

• $1 \leq N \leq 500$
• $1 \leq M \leq 500$
• $1 \leq Q \leq 500$
• $S_i$ is a string of length $M$ consisting of 0 and 1. $(1 \leq i \leq N)$
• $T_i$ is a string of length $M$ consisting of 0 and 1. $(1 \leq i \leq Q)$
• All input values are integers.

样例 1 解释：
$T_1$ 从一开始就被写在黑板上。

$T_2$ 是 001。若我们选择字符串 000、011、101 执行该操作，则可在黑板上新写出 001。

样例 2 解释：
黑板上初始写出的两个字符串均为 0，且通过该操作新写出的字符串也必为 0。因此，不可能使 1 出现在黑板上。

约束条件

• $1 \leq N \leq 500$
• $1 \leq M \leq 500$
• $1 \leq Q \leq 500$
• $S_i$ 是一个长度为 $M$、仅由字符 0 和 1 组成的字符串。$(1 \leq i \leq N)$
• $T_i$ 是一个长度为 $M$、仅由字符 0 和 1 组成的字符串。$(1 \leq i \leq Q)$
• 所有输入值均为整数。