You are given $$$n$$$ strings $$$s_1, s_2, \dots, s_n$$$, consisting of lowercase Latin letters. Let $$$|x|$$$ be the length of string $$$x$$$.
Let a collapse $$$C(a, b)$$$ of two strings $$$a$$$ and $$$b$$$ be the following operation:
Calculate $$$\sum\limits_{i=1}^n \sum\limits_{j=1}^n |C(s_i, s_j)|$$$.
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$).
Each of the next $$$n$$$ lines contains a string $$$s_i$$$ ($$$1 \le |s_i| \le 10^6$$$), consisting of lowercase Latin letters.
The total length of the strings doesn't exceed $$$10^6$$$.
Print a single integer — $$$\sum\limits_{i=1}^n \sum\limits_{j=1}^n |C(s_i, s_j)|$$$.
3abaabba
20
5ababbabxxabxbabab
126
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