Problem Statement

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.

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.

Input

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

Output

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.