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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < ll(n); i++)

const int maxn = 1e6 + 5;
int child[maxn][26];
bool is_end[maxn];
int nxt = 1;

vector<int> adj[maxn];

int main() {
    int n;
    cin >> n;
    vector<string> strs(n);
    rep(i, n) {
        string& s = strs[i];
        cin >> s;
        reverse(s.begin(), s.end());
        int node = 0;
        for (char c : s) {
            adj[i].push_back(node);
            if (child[node][c - 'a'] == 0) {
                child[node][c - 'a'] = nxt++;
            }
            node = child[node][c - 'a'];
        }
        is_end[node] = true;
    }

    // subtract (s[i], s[i]) cases
    ll ans = -n;
    rep(i, n) {
        string& s = strs[i];
        set<char> suffix;
        int m = s.size();
        for (int j = m - 1; j >= 0; j--) {
            suffix.insert(s[j]);
            int node = adj[i][j];
            for (char c : suffix) {
                ans += is_end[child[node][c - 'a']];
            }
        }
    }
    cout << ans << endl;
}