Little Lovro likes to play games with words. During the last few weeks he realized that some words don't like each other.

The words A and B don't like each other if the word A is lexicographically before the word B, but the word B' is lexicographically before the word A', where X' stands for the word X reversed (if X="kamen" then X'="nemak"). For example, the words "lova" and "novac" like each other, but the words "aron" and "sunce" don't like each other.

Given some set of the words, we define  the degree of chaos of the set as  the number of pairs of different words that don't like each other.

Write a program that, given a set of words, finds the chaos degree for the set.

Input

The first line of input contains an integer N, 2 ≤ N ≤ 100 000.

Each of the following N lines contains one word – a sequence of at most 10 lowercase letters of the English alphabet ('a'-'z'). There will be no two identical words in the set.

Output

The first and only line of output should contain a single integer – the chaos degree of the given set of words.

Note: use 64-bit signed integer type (int64 in Pascal, long long in C/C++).

Sample

input 
 
2 
lopta 
kugla 
 
output 
 
0

input 
 
4 
lova 
novac 
aron 
sunce 
 
output 
 
3

input 
 
14 
branimir 
vladimir 
tom 
kruz 
bred 
pit 
zemlja 
nije 
ravna 
ploca 
ko 
je 
zapalio 
zito 
 
output 
 
48