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

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class MainClass
{
    static int[] dy = new int[4] { 0, 1, 0, -1 };
    static int[] dx = new int[4] { 1, 0, -1, 0 };
    static string[] dw = new string[4] { "R", "U", "L", "D" };
    static void Main()
    {
        var r = Console.ReadLine().Split().Select(_=>int.Parse(_)+1010 ).ToArray();
        var sp = new int[2] { r[1], r[0] };
        var gp = new int[2] { r[3], r[2] };

        var frags = new bool[2020, 2020];
        var que = new Queue<(int, int,int)>();
        que.Enqueue((sp[0], sp[1],1));

        string ans = "";

        for (int i = 0; i < 4; i++)
        {
            var d = new ValueTuple<int, int>();
            if (i % 2 == 0) d = (gp[0], gp[1]);
            else d = (sp[0], sp[1]);

            var nfrags = new int[2020, 2020];
            

            while (que.Count > 0)
            {
                var t = que.Dequeue();
                int y = t.Item1;
                int x = t.Item2;
                int c = t.Item3;
                nfrags[y,x] = c;

                for (int j = 0; j < 4; j++)
                {
                    int ny = y + dy[j];
                    int nx = x + dx[j];
                    int nc = c + 1;

                    if (!(0 <= ny && ny < 2020 && 0 <= nx && nx < 2020)) continue;
                    if (nfrags[ny,nx]!=0||frags[ny,nx]) continue;
                    nfrags[ny, nx] = nc;
                    que.Enqueue((ny, nx, nc));
                }

                if (nfrags[d.Item1, d.Item2] != 0)
                    break;
            }

            string sb = "";
            int sy = d.Item1;
            int sx = d.Item2;
            for (int j = nfrags[d.Item1,d.Item2]-1; j >= 1; j--)
            {
                for (int k = 0; k < 4; k++)
                {
                    int sdy = sy - dy[k];
                    int sdx = sx - dx[k];
                    if (nfrags[sdy, sdx] == j)
                    {
                        frags[sdy, sdx] = true;
                        sb = dw[k] + sb;
                        
                        sy = sdy;
                        sx = sdx;
                        break;
                    }
                }
            }

            ans += sb;
            frags[sp[0], sp[1]] = false;
            frags[gp[0], gp[1]] = false;
            que = new Queue<(int, int, int)>();
            que.Enqueue((d.Item1,d.Item2,1));
        }

        Console.WriteLine(ans);
    }
}