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.Linq;
using System.Text;
using static System.Math;
using static _20200313.Abc051_C.Cin;
using static _20200313.Abc051_C.Util;
using Pair = _20200313.Abc051_C.VTuple<long, long>;
using Graph = System.Collections.Generic.List<System.Collections.Generic.List<long>>;

namespace _20200313
{
    public class Abc051_C
    {
        public static void Main(string[] args)
        {
            int sx = ri;
            int sy = ri;
            int tx = ri;
            int ty = ri;
            int dx = tx - sx;
            int dy = ty - sy;
            string ans = string.Empty;
            if (dx != 0 && dy != 0)
            {
                // 1
                ans += new string((dx > 0) ? 'R' : 'L', Abs(dx));
                ans += new string((dy > 0) ? 'U' : 'D', Abs(dy));
                ans += new string((dx > 0) ? 'L' : 'R', Abs(dx));
                ans += new string((dy > 0) ? 'D' : 'U', Abs(dy));

                // 2
                ans += (dy > 0) ? 'D' : 'U';
                ans += new string((dx > 0) ? 'R' : 'L', Abs(dx) + 1);
                ans += new string((dy > 0) ? 'U' : 'D', Abs(dy) + 1);
                ans += (dx > 0) ? 'L' : 'R';
                
                ans += (dy > 0) ? 'U' : 'D';
                ans += new string((dx > 0) ? 'L' : 'R', Abs(dx) + 1);
                ans += new string((dy > 0) ? 'D' : 'U', Abs(dy) + 1);
                ans += (dx > 0) ? 'R' : 'L';
            }
            else if (dx == 0)
            {
                // 1
                ans += new string((dy > 0) ? 'U' : 'D', Abs(dy));
                ans += "R";
                ans += new string((dy > 0) ? 'D' : 'U', Abs(dy));
                ans += "LL";

                // 2
                ans += new string((dy > 0) ? 'U' : 'D', Abs(dy));
                ans += "RURR";
                ans += new string((dy > 0) ? 'D' : 'U', Abs(dy)+2);
                ans += "LLU";
            }
            else if (dy == 0)
            {
                // 1
                ans += new string((dx > 0) ? 'R' : 'L', Abs(dx));
                ans += "D";
                ans += new string((dx > 0) ? 'L' : 'R', Abs(dx));
                ans += "UU";

                // 2
                ans += new string((dx > 0) ? 'R' : 'L', Abs(dx));
                ans += "DRDD";
                ans += new string((dx > 0) ? 'L' : 'R', Abs(dx)+2);
                ans += "UUR";
            }

            Console.WriteLine(ans);
        }

        public struct VTuple<T1,T2>:System.IComparable<VTuple<T1,T2>>,System.IEquatable<VTuple<T1,T2>>{public T1 First;public T2 Second;public VTuple(T1 a,T2 b){First=a;Second=b;}public int CompareTo(VTuple<T1,T2>a){int b=Comparer<T1>.Default.Compare(First,a.First);if(b!=0)return b;return Comparer<T2>.Default.Compare(Second,a.Second);}public override bool Equals(object a){return a is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)a);}public bool Equals(VTuple<T1,T2>a){return EqualityComparer<T1>.Default.Equals(First,a.First)&&EqualityComparer<T2>.Default.Equals(Second,a.Second);}public override int GetHashCode(){int a=First!=null?First.GetHashCode():0;int b=Second!=null?Second.GetHashCode():0;uint c=((uint)a<<5)|((uint)a>>27);return((int)c+a)^b;}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{V i;static Func<V>j=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){var a=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(i());}public static long ReadLong(){return long.Parse(i());}public static double ReadDouble(){return double.Parse(i());}public static string ReadString(){return i();}public static int[]ReadIntArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){g=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long b){a=new long[b];for(int c=0;c<b;c++)a[c]=ReadLong();}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[,]ReadIntTable(int a,int b){g=null;int[,]c=new int[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadInt();}return c;}public static long[,]ReadLongTable(long a,long b){g=null;long[,]c=new long[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadLong();}return c;}public static char[,]ReadCharTable(int a,int b){g=null;char[,]c=new char[a,b];for(int d=0;d<a;d++){var e=ReadString();for(int f=0;f<b;f++)c[d,f]=e[f];}return c;}static string[]g;static int h;static string i(){if(g==null||g.Length<=h){g=Console.ReadLine().Split(' ');h=0;}return g[h++];}}
    }
}