Problem:
C: Common Palindromes

ICPC で良い成績を収めるには修行が欠かせない．うさぎは ICPC で勝ちたいので，今日も修行をすることにした．

今日の修行は，文字列中にある回文を探すことによって，文章から隠れたメッセージを読解する能力を高めようというものである．回文はたくさんあるかもしれないので，探すついでに個数も数えてしまいたい．

2 つの文字列 S, T が与えられるので，以下を満たす整数の組 (i, j, k, l) の個数を求めたい．

1 ≤ i ≤ j ≤ (S の長さ)．

1 ≤ k ≤ l ≤ (T の長さ)．

S の i 文字目から j 文字目までを取り出した部分文字列は，T の k 文字目から l 文字目までを取り出した部分文字列と同一であり，さらにこれらは回文 (左から読んでも右から読んでも同じになる文字列) となっている．

Input

S
T

文字列 S, T はともに長さが 1 以上 50,000 以下であり，アルファベット大文字からなる．

Output

条件を満たす整数の組 (i, j, k, l) の個数を 1 行に出力せよ．

Sample Input 1

ICPC
CPCPC

Sample Output 1

10

Sample Input 2

BABBAB
ABBA

Sample Output 2

14

Sample Input 3

MYON
USAGI

Sample Output 3

0

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using Number = System.Int64;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var s = rs;
            var t = rs;
            var str = s + "$%" + t;
            var tree = new PalindromicTree(str.ToArray());
            long ans = 0;
            for (int i = 2; i < tree.nodes.Length; i++)
            {
                if (tree.nodes[i] != null)
                    ans += Math.BigMul(tree.nodes[i].freq[0], tree.nodes[i].freq[1]);
            }
            Console.WriteLine(ans);
        }
        const long INF = 1L << 60;
        //int[] dx = { -1, 0, 1, 0 };
        //int[] dy = { 0, 1, 0, -1 };
        //*
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        //*/

        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ")
    {
        return string.Join(st, ie.Select(x => x.ToString()).ToArray());
        //return string.Join(st, ie);
    }
    static public void Main()
    {
        Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read())
                if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}
#endregion
#region Palindromic Tree
public class PalindromicTree
{
    public Node[] nodes;
    public PalindromicTree(char[] s)
    {
        var n = s.Length;
        var zero = new Node(-1, 0, (char)0, 1);
        var hell = new Node(-1, -1, (char)0, 0);
        zero.link = hell.link = hell;
        hell.Add(zero);
        nodes = new Node[n + 2];
        var ptr = 0;
        nodes[ptr++] = hell;
        nodes[ptr++] = zero;
        var cur = zero;//current suffix
        var px = 0;
        for (int i = 0; i < n; i++)
        {
            var x = s[i];
            while (i - cur.len - 1 < 0 || s[i - cur.len - 1] != x)//find xAx
            {
                cur = cur.link;
            }
            var xax = cur.Next(x);//already exists
            if (xax == null)
            {
                //new subpalindrome
                xax = new Node(i - cur.len - 1, cur.len + 2, x, ptr);
                nodes[ptr++] = xax;
                cur.Add(xax);

                //make suffix link
                if (xax.len == 1)
                    xax.link = zero;
                else
                {
                    var b = cur.link;
                    while (true)
                    {
                        while (i - b.len < 0 || s[i - b.len - 1] != x) //find xBx
                        {
                            b = b.link;
                        }
                        var xbx = b.Next(x);
                        if (xbx != null)
                        {
                            xax.link = xbx;
                            break;
                        }
                    }
                }
            }
            if (s[i] == '$') px++;
            if (s[i] != '$' && s[i] != '%') xax.freq[px]++;
            cur = xax;
        }
        for (int i = ptr - 1; i >= 2; i--)
        {
            nodes[i].link.freq[0] += nodes[i].freq[0];
            nodes[i].link.freq[1] += nodes[i].freq[1];
        }

    }
    public class Node
    {
        public int id, first, len;
        public int[] freq = new int[2];
        public char c;
        public Node firstChild;
        public Node sibling;
        public Node link;
        public Node(int first, int len, char c, int id)
        {
            this.first = first;
            this.len = len;
            this.c = c;
            this.id = id;
        }
        public Node Next(char c)
        {
            for (Node ch = firstChild; ch != null; ch = ch.sibling)
                if (ch.c == c) return ch;
            return null;
        }
        public void Add(Node x)
        {
            var ch = firstChild;
            firstChild = x;
            x.sibling = ch;
        }


        public override string ToString()
        {
            return string.Format("Node [id={0}, first={1}, len={2}, freq={7}, c={3}, firstchild={4}, sibling={5}, link={6}]", id, first, len, c, firstChild != null ? firstChild.id : -1, sibling != null ? sibling.id : -1, link != null ? link.id : -1, freq);
        }
    }

}
#endregion