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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;

class Solver
{
    public Scanner sc;
    public void Solve()
    {
        var N = sc.Int;
        var ct = Create(26, () => new Dictionary<ulong, int>());
        var S = Create(N, () => sc.Str.ToCharArray());
        Array.Sort(S, (a, b) => a.Length - b.Length);
        var res = 0L;
        foreach (var s in S)
        {
            var r = new RollingHash(s);
            var c = new int[26];
            for (int i = 0; i < s.Length; i++)
            {
                c[s[i] - 'a']++;
            }
            for (int i = s.Length - 1; i >= 0; i--)
            {
                for (int j = 0; j < 26; j++)
                    if (c[j] > 0)
                    {
                        var hash = r.GetHash(i + 1, s.Length);
                        if (!ct[j].ContainsKey(hash))
                            continue;
                        res += ct[j][hash];
                    }
                c[s[i] - 'a']--;
            }
            var hs = r.GetHash(1, s.Length);
            if (!ct[s[0] - 'a'].ContainsKey(hs))
                ct[s[0] - 'a'][hs] = 0;
            ct[s[0] - 'a'][hs]++;
        }
        Console.WriteLine(res);
    }
}

public class RollingHash
{
    public char[] str { get; }
    private ulong[] hashTable;
    private static ulong[] pow;
    private static uint Base { get; }
    const ulong MASK30 = (1UL << 30) - 1;
    const ulong MASK31 = (1UL << 31) - 1;
    private const ulong MOD = (1UL << 61) - 1;
    public RollingHash(char[] str)
    {
        this.str = str;
        hashTable = new ulong[str.Length + 1];
        for (var j = 1; j <= str.Length; j++)
            hashTable[j] = CalcMod(Mul(hashTable[j - 1], Base) + str[j - 1]);
    }
    static RollingHash()
    {
        var rnd = new Random(); int min = 150, max = int.MaxValue;
        Base = (uint)rnd.Next(min, max);
        pow = new ulong[1001001];
        pow[0] = 1;
        for (var j = 1; j < pow.Length; j++)
            pow[j] = Mul(pow[j - 1], Base);
    }
    public ulong insert(char c, int l, int r)
    {
        return CalcMod(GetHash(l, r) + Mul(pow[r - l], c));
    }
    private static ulong Mul(ulong a, ulong b)
    {
        var au = a >> 31;
        var ad = a & MASK31;
        var bu = b >> 31;
        var bd = b & MASK31;
        var mid = ad * bu + au * bd;
        var midu = mid >> 30;
        var midd = (mid & MASK30);
        return CalcMod(au * bu * 2 + midu + (midd << 31) + ad * bd);
    }
    private static ulong CalcMod(ulong val)
    {
        val = (val & MOD) + (val >> 61);
        if (val > MOD) val -= MOD;
        return val;
    }

    public ulong GetHash(int l = 0, int r = -1)
    {
        if (r < 0) r = str.Length;
        return CalcMod(hashTable[r] + MOD * ((1UL << 3) - 1) - Mul(hashTable[l], pow[r - l]));
    }
    //thisの[l1:)とhの[l2:)のLCP
    public int LCP(RollingHash h, int l1 = 0, int l2 = 0)
    {
        int l = 0, r = Min(str.Length - l1, h.str.Length - l2) + 1;
        while (r - l > 1)
        {
            var m = (r + l) / 2;
            if (GetHash(l1, l1 + m) == h.GetHash(l2, l2 + m)) l = m;
            else r = m;
        }
        return l;
    }
    public int LCP(int l1 = 0, int l2 = 0) => LCP(this, l1, l2);
}
#region Template
public static class Template
{
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver() { sc = new Scanner() };
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        sol.Solve();
        Console.Out.Flush();
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static void Out<T>(this IList<T> A, out T a) => a = A[0];
    public static void Out<T>(this IList<T> A, out T a, out T b) { a = A[0]; b = A[1]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c) { A.Out(out a, out b); c = A[2]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c, out T d) { A.Out(out a, out b, out c); d = A[3]; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static char ToChar(this int s, char begin = '0') => (char)(s + begin);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion