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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define IO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
const int N=1e6+2;
int trie[N][27], nxt, freq[N], first[30] , n;
ll ans;
void solve(string & s)
{
    int sz=s.size();
    for(int i=0; i<26; i++)
        first[i]=1e7;
    for(int i=0; i<sz; i++)
        first[s[i]-'a']=min(first[s[i]-'a'],i);
    int node=0;
    for(int i=sz-1; i>=0; i--)
    {
        for(int j=0; j<26; j++)
            if(first[j]<=i)
                ans+=freq[trie[node][j]];
        node=trie[node][s[i]-'a'];
    }
}
vector<string> v;
int main()
{
    IO
    cin>>n;
    while(n--)
    {
        string s;
        cin>>s;
        int sz=s.size();
        v.push_back(s);
        int node=0;
        for(int i=sz-1; i>=0; i--)
        {
            if(trie[node][s[i]-'a']==0)
                trie[node][s[i]-'a']=++nxt;
            node=trie[node][s[i]-'a'];
        }
        freq[node]++;
        ans-=freq[node];
    }
    for(auto &i : v)
        solve(i);
    cout<<ans;
}