Problem:
Score : 700 points

Problem Statement

Limak can repeatedly remove one of the first two characters of a string,
for example abcxyx \rightarrow acxyx \rightarrow cxyx \rightarrow cyx.

You are given N different strings S_1, S_2, \ldots, S_N.
Among N \cdot (N-1) / 2 pairs (S_i, S_j),
in how many pairs could Limak obtain one string from the other?

Constraints

2 \leq N \leq 200\,000

S_i consists of lowercase English letters a-z.

S_i \neq S_j

1 \leq |S_i|

|S_1| + |S_2| + \ldots + |S_N| \leq 10^6

Input

Input is given from Standard Input in the following format.

N
S_1
S_2
\vdots
S_N

Output

Print the number of unordered pairs (S_i, S_j)
where i \neq j and Limak can obtain one string from the other.

Sample Input 1

3
abcxyx
cyx
abc

Sample Output 1

1

The only good pair is (abcxyx, cyx).

Sample Input 2

6
b
a
abc
c
d
ab

Sample Output 2

5

There are five good pairs: (b, abc), (a, abc), (abc, c), (b, ab), (a, ab).

Solution in C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class B
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var ss = new int[n].Select(_ => Console.ReadLine()).OrderBy(s => s.Length).ToArray();

		var r = 0L;
		var root = new Node();

		foreach (var s in ss)
		{
			var node = root;
			for (int i = s.Length - 1; i >= 0; i--)
			{
				if (i == 0)
					if (node.Ends.ContainsKey(s[i])) node.Ends[s[i]]++;
					else node.Ends[s[i]] = 1;
				else
					foreach (var (c, v) in node.Ends)
						if (s.IndexOf(c, 0, i + 1) >= 0) r += v;

				if (!node.Nexts.ContainsKey(s[i]))
					node.Nexts[s[i]] = new Node();
				node = node.Nexts[s[i]];
			}
		}

		Console.WriteLine(r);
	}
}

class Node
{
	public Dictionary<char, int> Ends = new Dictionary<char, int>();
	public Dictionary<char, Node> Nexts = new Dictionary<char, Node>();
}