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You, a perfect speller, have a vocabulary of \(N\) distinct words, \(V_1, ..., V_N\), each consisting of exactly \(L\) lowercase letters from the alphabet \(\{\)`'m'`, `'e'`, `'t'`, `'a'`\(\}\).
Your friend, a truely terrable speler, has attempted to write \(Q\) of these words as \(W_1, ..., W_Q\), each also consisting of \(L\) lowercase letters from the same alphabet.
Let \(S_i\) be the number of words in your vocabulary that differ from \(W_i\) at exactly two indices. Please determine the sum \(S_1 + ... + S_Q\).
# Constraints
\(1 \le T \le 95\)
\(1 \le N, Q \le 750{,}000\)
\(1 \le L = |V_i| = |W_i| \le 20{,}000\)
\((N+Q)*L \le 15{,}000{,}000\)
\(V_{ij} \in \{\)`'m'`, `'e'`, `'t'`, `'a'`\(\}\)
\(W_{ij} \in \{\)`'m'`, `'e'`, `'t'`, `'a'`\(\}\)
All \(V_i\) in a given test case are distinct.
The sum of lengths of all strings across all cases is at most \(18{,}000{,}000\).
# Input Format
Input begins with a single integer \(T\), the number of test cases. For each test case, there is first a line containing a single integer \(N\). Then, \(N\) lines follow, the \(i\)th of which contains the string \(V_i\). Then, there is a line containing a single integer \(Q\). Then, \(Q\) lines follow, the \(i\)th of which contains the string \(W_i\).
# Output Format
For the \(i\)th test case, output a single line containing `"Case #i: "` followed by a single integer, the sum \(S_1 + ... + S_Q\).
# Sample Explanation
The first case is depicted below:
{{PHOTO_ID:1332823754208247|WIDTH:500}}
The answer is \(4\), since:
- \(W_1\) = "`teammate`" differs from "`metamate`" at three indices, so \(S_1 = 0\).
- \(W_2\) = "`meatmate`" differs from "`metamate`" at exactly two indices, so \(S_2 = 1\).
- \(W_3\) = "`metatame`" differs from "`metamate`" at exactly two indices, so \(S_3 = 1\).
- \(W_4\) = "`mememate`" differs from "`metamate`" at exactly two indices, so \(S_4 = 1\).
- \(W_5\) = "`metameme`" differs from "`metamate`" at exactly two indices, so \(S_5 = 1\).
In the second case, the answer is \(0\), since:
- \(W_1\) = "`tata`" differs from \(V_1\) = "`meet`" at four indices, \(V_2\) = "`emma`" at three indices, and \(V_3\) = "`tate`" at only one index, so \(S_1 = 0\).
- \(W_2\) = "`maam`" differs from \(V_1\) = "`meet`" at three indices, \(V_2\) = "`emma`" at four indices, and \(V_3\) = "`tate`" at three indices, so \(S_2 = 0\).
In the third case, the answer is \(5\), since:
- \(W_1\) = "`tam`" differs from both \(V_1\) = "`mem`" and \(V_3\) = "`mat`" at exactly two indices, so \(S_1 = 2\).
- \(W_2\) = "`mat`" differs from \(V_1\) = "`mem`" at exactly two indices, so \(S_2 = 1\).
- \(W_3\) = "`tea`" differs from both \(V_1\) = "`mem`" and \(V_2\) = "met" at exactly two indices, so \(S_3 = 2\).
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