Problem:
Score : 300 points

Problem Statement

Dolphin resides in two-dimensional Cartesian plane, with the positive x-axis pointing right and the positive y-axis pointing up.

Currently, he is located at the point (sx,sy). In each second, he can move up, down, left or right by a distance of 1.

Here, both the x- and y-coordinates before and after each movement must be integers.

He will first visit the point (tx,ty) where sx < tx and sy < ty, then go back to the point (sx,sy), then visit the point (tx,ty) again, and lastly go back to the point (sx,sy).

Here, during the whole travel, he is not allowed to pass through the same point more than once, except the points (sx,sy) and (tx,ty).

Under this condition, find a shortest path for him.

Constraints

-1000 ≤ sx < tx ≤ 1000

-1000 ≤ sy < ty ≤ 1000

sx,sy,tx and ty are integers.

Input

The input is given from Standard Input in the following format:

sx sy tx ty

Output

Print a string S that represents a shortest path for Dolphin.

The i-th character in S should correspond to his i-th movement.

The directions of the movements should be indicated by the following characters:

U: Up

D: Down

L: Left

R: Right

If there exist multiple shortest paths under the condition, print any of them.

Sample Input 1

0 0 1 2

Sample Output 1

UURDDLLUUURRDRDDDLLU

One possible shortest path is:

Going from (sx,sy) to (tx,ty) for the first time: (0,0) → (0,1) → (0,2) → (1,2)

Going from (tx,ty) to (sx,sy) for the first time: (1,2) → (1,1) → (1,0) → (0,0)

Going from (sx,sy) to (tx,ty) for the second time: (0,0) → (-1,0) → (-1,1) → (-1,2) → (-1,3) → (0,3) → (1,3) → (1,2)

Going from (tx,ty) to (sx,sy) for the second time: (1,2) → (2,2) → (2,1) → (2,0) → (2,-1) → (1,-1) → (0,-1) → (0,0)

Sample Input 2

-2 -2 1 1

Sample Output 2

UURRURRDDDLLDLLULUUURRURRDDDLLDL

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    partial class Program
    {
        static long mod = 1000000007;
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Console.Out.Flush();
            Console.ReadKey();
        }

        //ここから


        static void Solve()
        {
            int sx;int sy;int tx;int ty;
            Multi(out sx, out sy, out tx, out ty);
            string S = "";
            S += new string(Enumerable.Repeat('U', ty - sy).ToArray());
            S += new string(Enumerable.Repeat('R', tx - sx).ToArray());
            S += new string(Enumerable.Repeat('D', ty - sy).ToArray());
            S += new string(Enumerable.Repeat('L', tx - sx + 1).ToArray());
            S += new string(Enumerable.Repeat('U', ty - sy + 1).ToArray());
            S += new string(Enumerable.Repeat('R', tx - sx + 1).ToArray());
            S += "DR";
            S += new string(Enumerable.Repeat('D', ty - sy + 1).ToArray());
            S += new string(Enumerable.Repeat('L', tx - sx + 1).ToArray());
            S += "U";



            Console.WriteLine(S);
        }
    }


    //拡張メソッド
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }
    }

    partial class Program
    {
        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public char GetChar() { return Console.ReadLine().Trim()[0]; }
        static public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        static public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        static public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        static public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        static public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        static public void WriteObjects<T>(IList<T> values) { var num = values.Count; for (int i = 0; i < num; i++) { Console.Write(values[i]); if (i < num - 1) { Console.Write(" "); } } Console.WriteLine(); }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
    }
}