KAOS - Kaos

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++)

Examples

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

Added by:Filip Karlo Došilović
Date:2015-09-17
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 MAWK BC NCSHARP COFFEE DART FORTH GOSU JS-MONKEY JULIA KTLN OCT PROLOG PYPY3 R RACKET SQLITE SWIFT UNLAMBDA
Resource:COI, 2006, 2nd Day, Seniors

hide comments
2018-06-07 14:49:24
When you are the 100th buddy to solve this question.
AC in one go :D mergesort did it's work!
2015-10-29 14:12:03 Filip K. Dosilovic
@mehmetinal @cricycle problem was added because time limit on MCHAOS is not official time limit for the problem
2015-10-27 04:38:51 Alex Anderson
@mehmetin, you're right. I think this problem should be removed.
2015-10-06 11:20:18 mehmetin
This problem is the exact duplicate of MCHAOS. Only difference is the relaxed time limit.

Last edit: 2015-10-06 11:25:33
2015-09-30 16:24:14 matematikaadit
a copy-paste-friendly version of examples above:

2
lopta
kugla

4
lova
novac
aron
sunce

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

2015-09-21 21:01:27 Filip K. Dosilovic
@SRC: no, there is no space.

Last edit: 2015-09-28 18:41:18
2015-09-19 17:15:59 SRC
is that a space before lova and novac in the 2nd example?
2015-09-18 10:25:47 miodziu
@ravi12345: Empty words are not allowed.
2015-09-18 10:22:00 miodziu
My ACC solution gives result 47 in 3rd example. Also my brute-force algorithm gives 47 in this example :)
2015-09-18 08:26:32
empty words are allowed or not?
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