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-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		var dic = new Dictionary<string,int>[1000001];
		for(var i=0;i<=1000000;i++){
			dic[i] = new Dictionary<string,int>();
		}
		for(var i=0;i<N;i++){
			string s = Console.ReadLine();
			int l = s.Length;
			if(dic[l].ContainsKey(s)){
				dic[l][s]++;
			} else {
				dic[l][s] = 1;
			}
		}
		long ans = 0;
		for(var i=0;i<=1000000;i++){
			foreach(var d in dic[i].Keys){
				for(var j=0;j<=i;j++){
					foreach(var e in dic[j].Keys){
						int d1 = d.Length-1;
						int e1 = e.Length-1;
						int ct = 0;
						bool flag = true;
						bool flag2 = true;
						while(true){
							if(d.Substring(d1,1)==e.Substring(e1,1)){
								d1--;
								e1--;
								if(e1==-1){
									break;
								}
								if(d1==-1){
									flag2 = false;
									break;
								}
							} else {
								d1--;
								if(d1<0){
 									flag2 = false;
                                  	break;
								}
								if(flag==false){
									flag2 = false;
									break;
								} else {
									flag = false;
								}
							}
						}
						if(flag2){
							ans++;
						}
					}
				}
			}
		}
		Console.WriteLine(ans-N);
	}
}