Bijective Mapping Check

You are given a pattern string S and a string of space-separated words. Your task is to determine if there exists a bijective mapping between letters in the pattern and the words. A bijective mapping means that each unique letter in the pattern is mapped to a unique word and vice versa.

Formally, given a pattern \(S\) of length \(n\) and a list of words \(W\) of length \(n\), there exists a bijective mapping if and only if for every index \(i\) (\(1 \leq i \leq n\)), the mapping satisfies:

[ \text{if } S_i = S_j \text{ then } W_i = W_j, \quad \text{and if } S_i \neq S_j \text{ then } W_i \neq W_j. ]

You will be given several test cases as input through stdin, and for each test case you should print a single line with the result (true or false) to stdout.

inputFormat

The input is given via stdin in the following format:

T
pattern_1
words_1
pattern_2
words_2
... 
pattern_T
words_T

Where:

• T is the number of test cases.
• For each test case, the first line is the pattern string and the second line is a space‐separated list of words.

outputFormat

For each test case, print a single line to stdout with either true if a bijective mapping exists between the pattern and the list of words, or false otherwise.

## sample

2
abba
dog cat cat dog
abba
dog cat cat fish

true
false

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