CF1669E 2-Letter Strings

Given $ n $ strings, each of length $ 2 $ , consisting of lowercase Latin alphabet letters from 'a' to 'k', output the number of pairs of indices $ (i, j) $ such that $ i < j $ and the $ i $ -th string and the $ j $ -th string differ in exactly one position. In other words, count the number of pairs $ (i, j) $ ( $ i < j $ ) such that the $ i $ -th string and the $ j $ -th string have exactly one position $ p $ ( $ 1 \leq p \leq 2 $ ) such that $ {s_{i}}_{p} \neq {s_{j}}_{p} $ . The answer may not fit into 32-bit integer type, so you should use 64-bit integers like long long in C++ to avoid integer overflow.

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the number of strings. Then follows $ n $ lines, the $ i $ -th of which containing a single string $ s_i $ of length $ 2 $ , consisting of lowercase Latin letters from 'a' to 'k'. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, print a single integer — the number of pairs $ (i, j) $ ( $ i < j $ ) such that the $ i $ -th string and the $ j $ -th string have exactly one position $ p $ ( $ 1 \leq p \leq 2 $ ) such that $ {s_{i}}_{p} \neq {s_{j}}_{p} $ . Please note, that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

For the first test case the pairs that differ in exactly one position are: ("ab", "cb"), ("ab", "db"), ("ab", "aa"), ("cb", "db") and ("cb", "cc"). For the second test case the pairs that differ in exactly one position are: ("aa", "ac"), ("aa", "ca"), ("cc", "ac"), ("cc", "ca"), ("ac", "aa") and ("ca", "aa"). For the third test case, the are no pairs satisfying the conditions.