Dasha and Nightmares

题意翻译

给定 $n$ 和 $n$ 个字符串 $s_i$。 问有多少对不同的 $\langle i,j\rangle(1\leq i\leq j\leq n)$，使得 $s_i$ 和 $s_j$ 拼接后的字符串满足下列条件： - 长度为奇数 - 恰好出现 $25$ 个字母 - 每个字母出现次数为奇数 $1\leq n\leq2\times10^5,\sum\limits_{i=1}^n \left\vert s_i\right\vert\leq5\times10^6$ by @Larryyu

题目描述

Dasha, an excellent student, is studying at the best mathematical lyceum in the country. Recently, a mysterious stranger brought $ n $ words consisting of small latin letters $ s_1, s_2, \ldots, s_n $ to the lyceum. Since that day, Dasha has been tormented by nightmares. Consider some pair of integers $ \langle i, j \rangle $ ( $ 1 \le i \le j \le n $ ). A nightmare is a string for which it is true: - It is obtained by concatenation $ s_{i}s_{j} $ ; - Its length is odd; - The number of different letters in it is exactly $ 25 $ ; - The number of occurrences of each letter that is in the word is odd. For example, if $ s_i= $ "abcdefg" and $ s_j= $ "ijklmnopqrstuvwxyz", the pair $ \langle i, j \rangle $ creates a nightmare. Dasha will stop having nightmares if she counts their number. There are too many nightmares, so Dasha needs your help. Count the number of different nightmares. Nightmares are called different if the corresponding pairs $ \langle i, j \rangle $ are different. The pairs $ \langle i_1, j_1 \rangle $ and $ \langle i_2, j_2 \rangle $ are called different if $ i_1 \neq i_2 $ or $ j_1 \neq j_2 $ .

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of words. The following $ n $ lines contain the words $ s_1, s_2, \ldots, s_n $ , consisting of small latin letters. It is guaranteed that the total length of words does not exceed $ 5 \cdot 10^6 $ .

输出格式

Print a single integer — the number of different nightmares.

输入输出样例

输入样例 #1

10
ftl
abcdefghijklmnopqrstuvwxy
abcdeffghijkllmnopqrsttuvwxy
ffftl
aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyy
thedevid
bcdefghhiiiijklmnopqrsuwxyz
gorillasilverback
abcdefg
ijklmnopqrstuvwxyz

输出样例 #1

5

说明

In the first test, nightmares are created by pairs $ \langle 1, 3 \rangle $ , $ \langle 2, 5 \rangle $ , $ \langle 3, 4 \rangle $ , $ \langle 6, 7 \rangle $ , $ \langle 9, 10 \rangle $ .