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 lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }
template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x)
#endif

// Rolling Hash (Rabin-Karp), 1dim
template<typename V>
struct rolling_hash
{
    V B;
    vector<V> hash; // hash[i] = s[0] * B^(i - 1) + ... + s[i - 1]
    vector<V> power; // power[i] = B^i
    rolling_hash() {}
    rolling_hash(const string &s, V b) : B(b)
    {
        int N = s.length();
        hash.resize(N + 1), power.resize(N + 1, 1);
        for (int i = 0; i < N; i++)
        {
            power[i + 1] = power[i] * B;
            hash[i + 1] = hash[i] * B + s[i];
        }
    }
    V get_hash(int l, int r) // s[l] * B^(r - l - 1) + ... + s[r - 1]
    {
        return hash[r] - hash[l] * power[r - l];
    }
};

using lint = long long;
using plint = pair<lint, lint>;
struct DoubleHash : public plint
{
    static plint MODs;
    DoubleHash(plint x) : plint(x) {}
    DoubleHash(lint x, lint y) : plint(x, y) {}
    DoubleHash(lint x) : DoubleHash(x, x) {}
    DoubleHash() : DoubleHash(0) {}
    static inline DoubleHash mod_subtract(plint x)
    {
        if (x.first >= MODs.first) x.first -= MODs.first;
        if (x.second >= MODs.second) x.second -= MODs.second;
        return x;
    }
    DoubleHash operator+(const DoubleHash &x) const
    {
        return mod_subtract(plint(this->first + x.first, this->second + x.second));
    }
    DoubleHash operator+(lint x) const
    {
        return mod_subtract(plint(this->first + x, this->second + x));
    }
    DoubleHash operator-(const DoubleHash &x) const
    {
        return mod_subtract(plint(this->first - x.first + MODs.first, this->second - x.second + MODs.second));
    }
    DoubleHash operator*(const DoubleHash &x) const
    {
        return make_pair(this->first * x.first % MODs.first, this->second * x.second % MODs.second);
    }
    DoubleHash operator*(lint x) const
    {
        return make_pair(this->first * x % MODs.first, this->second * x % MODs.second);
    }
};
plint DoubleHash::MODs = plint(1000000007, 998244353);
const DoubleHash b(8e7, 5e8);

int main()
{
    int N;
    cin >> N;
    vector<pair<size_t, string>> VS;
    REP(i, N)
    {
        string s;
        cin >> s;
        VS.emplace_back(s.length(), s);
    }
    sort(VS.begin(), VS.end());

    vector<set<DoubleHash>> dh(26);

    int ret = 0;
    for (auto [len, S] : VS)
    {
        rolling_hash<DoubleHash> rh(S, b);
        vector<int> vis(26);
        REP(i, S.length())
        {
            vis[S[i] - 'a'] = 1;
            auto h = rh.get_hash(i + 1, S.length());
            REP(d, 26) if (vis[d] and dh[d].count(h)) ret++;
        }
        dh[S[0] - 'a'].insert(rh.get_hash(1, S.length()));
    }
    cout << ret << '\n';
}