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;
 
using ll = long long;
constexpr ll mod = 387947498641LL;
#define endl '\n'


int main() {
  ios::sync_with_stdio(0); cin.tie(0);
 
  ll n;
  cin >> n;
  vector<string> A(n);
  for (auto& _a : A) cin >> _a;
  map<int64_t, array<ll,26>> cnt;
  for (auto& s : A) {
    int c = s[0]-'a';
    int ns = s.length();
    ll x = 0;
    for (int i = ns-1; i >= 1; --i) x = (x*27 + (s[i]-'a'+1)) % mod;
    ++cnt[x][c];
  }
  

  vector<int> n_char(26);
  ll ans = 0;
  for (auto& s : A) {
    int ns = s.length();
    fill(n_char.begin(), n_char.end(), 0);
    for (int i = 0; i < ns; ++i) ++n_char[s[i]-'a'];

    ll x = 0;
    for (int i = ns; i >= 1; --i) {
      if (i < ns) {
        --n_char[s[i]-'a'];
        x = (x*27 + (s[i]-'a'+1)) % mod;
      }
      auto it = cnt.find(x);
      if (it != cnt.end()) {
        for (int c = 0; c < 26; ++c) {
          if (it->second[c] && n_char[c]) {
            ++ans;
          }
        }
      }
    }
  }
  ans -= n;
  ans = max(ans, 0LL);
  cout << ans << endl;
}