Colliding Encoding

Alan just had his first cryptography class in school today. He decided to apply what he learned and came up with his own cipher. He maps each English letter from A to Z to a decimal digit from $0$ to $9$. He then encodes each word as a string of decimal digits by replacing each letter with its mapped digit.

Alan did not notice that there are $26$ letters and only $10$ decimal digits. As a result, collisions are possible, meaning two different words can have the same encoding.

Given a list of $N$ words and the mapping Alan uses, determine whether any collisions exist among the words on the list.

The first line of the input contains the number of test cases, $T$. Then $T$ test cases follow.

The first line of each test case contains 26 decimal digits (integers from $0$ to $9$, inclusive) $D_A, D_B, \dots, D_Z$. Letter $\alpha$ is mapped to digit $D_\alpha$.

The second line of each test case contains $N$, the number of words.

Each of the next $N$ lines contains one word $S_i$.

For each test case, output one line containing Case #x: y, where $x$ is the test case number starting from 1. Output YES if at least one pair of different words on the list has the same encoding. Otherwise, output NO.

• $1 \le T \le 100$.
• $0 \le D_\alpha \le 9$ for all letters $\alpha$.
• $1 \le$ the length of $S_i \le 10$ for all $i$.
• Each character of $S_i$ is an uppercase English letter from A to Z.
• $S_i \ne S_j$ for all $i \ne j$.

In Sample Case #1, the mapping for A is $0$, for B is $1$, for C is $2$, for D is $3$, and for E is $3$. With this mapping, ABC is encoded as $012$, BC is encoded as $12$, BCD as $123$, and CDE as $233$. Since all of these encodings are distinct, there are no collisions.

In Sample Case #2, the mapping for C is $2$, for D is $3$, for E is $3$, for F is $3$, and for G is $3$. With this mapping, CDE is encoded as $233$, DEF as $333$, and EFG as $333$. Since the encodings for DEF and EFG are the same, there is a collision.