F. String Distance
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Suppose you are given two strings $$$a$$$ and $$$b$$$. You can apply the following operation any number of times: choose any contiguous substring of $$$a$$$ or $$$b$$$, and sort the characters in it in non-descending order. Let $$$f(a, b)$$$ the minimum number of operations you have to apply in order to make them equal (or $$$f(a, b) = 1337$$$ if it is impossible to make $$$a$$$ and $$$b$$$ equal using these operations).

For example:

  • $$$f(\text{ab}, \text{ab}) = 0$$$;
  • $$$f(\text{ba}, \text{ab}) = 1$$$ (in one operation, we can sort the whole first string);
  • $$$f(\text{ebcda}, \text{ecdba}) = 1$$$ (in one operation, we can sort the substring of the second string starting from the $$$2$$$-nd character and ending with the $$$4$$$-th character);
  • $$$f(\text{a}, \text{b}) = 1337$$$.

You are given $$$n$$$ strings $$$s_1, s_2, \dots, s_k$$$ having equal length. Calculate $$$\sum \limits_{i = 1}^{n} \sum\limits_{j = i + 1}^{n} f(s_i, s_j)$$$.

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of strings.

Then $$$n$$$ lines follow, each line contains one of the strings $$$s_i$$$, consisting of lowercase Latin letters. $$$|s_1| = |s_2| = \ldots = |s_n|$$$, and $$$n \cdot |s_1| \le 2 \cdot 10^5$$$. All these strings are pairwise distinct.

Output

Print one integer: $$$\sum \limits_{i = 1}^{n} \sum\limits_{j = i + 1}^{n} f(s_i, s_j)$$$.

Examples
Input
4
zzz
bac
abc
acb
Output
4015
Input
2
a
b
Output
1337