Problem: Nash designed an interesting yet simple board game where a player is simply required to follow instructions written on the cell where the player currently stands. 

This board game is played on the n× n board. Rows and columns of this board are numbered from 1 to n. The cell on the intersection of the r-th row and c-th column is denoted by (r, c).

Some cells on the board are called blocked zones. On each cell of the board, there is written one of the following 5 characters — U, D, L, R or X — instructions for the player. Suppose that the current cell is (r, c). If the character is R, the player should move to the right cell (r, c+1), for L the player should move to the left cell (r, c-1), for U the player should move to the top cell (r-1, c), for D the player should move to the bottom cell (r+1, c). Finally, if the character in the cell is X, then this cell is the blocked zone. The player should remain in this cell (the game for him isn't very interesting from now on).

It is guaranteed that the characters are written in a way that the player will never have to step outside of the board, no matter at which cell he starts.

As a player starts from a cell, he moves according to the character in the current cell. The player keeps moving until he lands in a blocked zone. It is also possible that the player will keep moving infinitely long.

For every of the n^2 cells of the board Alice, your friend, wants to know, how will the game go, if the player starts in this cell. For each starting cell of the board, she writes down the cell that the player stops at, or that the player never stops at all. She gives you the information she has written: for each cell (r, c) she wrote: 

  * a pair (x,y), meaning if a player had started at (r, c), he would end up at cell (x,y). 
  * or a pair (-1,-1), meaning if a player had started at (r, c), he would keep moving infinitely long and would never enter the blocked zone. 



It might be possible that Alice is trying to fool you and there's no possible grid that satisfies all the constraints Alice gave you. For the given information Alice provided you, you are required to decipher a possible board, or to determine that such a board doesn't exist. If there exist several different boards that satisfy the provided information, you can find any of them.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 10^{3}) — the side of the board.

The i-th of the next n lines of the input contains 2n integers x_1, y_1, x_2, y_2, ..., x_n, y_n, where (x_j, y_j) (1 ≤ x_j ≤ n, 1 ≤ y_j ≤ n, or (x_j,y_j)=(-1,-1)) is the pair written by Alice for the cell (i, j). 

Output

If there doesn't exist a board satisfying the information that Alice gave you, print a single line containing INVALID. 

Otherwise, in the first line print VALID. In the i-th of the next n lines, print the string of n characters, corresponding to the characters in the i-th row of the suitable board you found. Each character of a string can either be U, D, L, R or X. If there exist several different boards that satisfy the provided information, you can find any of them.

Examples

Input


2
1 1 1 1
2 2 2 2


Output


VALID
XL
RX


Input


3
-1 -1 -1 -1 -1 -1
-1 -1 2 2 -1 -1
-1 -1 -1 -1 -1 -1


Output


VALID
RRD
UXD
ULL

Note

For the sample test 1 :

The given grid in output is a valid one. 

  * If the player starts at (1,1), he doesn't move any further following X and stops there. 
  * If the player starts at (1,2), he moves to left following L and stops at (1,1). 
  * If the player starts at (2,1), he moves to right following R and stops at (2,2). 
  * If the player starts at (2,2), he doesn't move any further following X and stops there. 



The simulation can be seen below : 

<image>

For the sample test 2 : 

The given grid in output is a valid one, as a player starting at any cell other than the one at center (2,2), keeps moving in an infinitely long cycle and never stops. Had he started at (2,2), he wouldn't have moved further following instruction X .

The simulation can be seen below : 

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main{
  static int repow(int b,int p){
    long a = b;
    long res=1;
    while(p>0){
      if(p%2==1){
        res*=a;
      }
      a*=a;
      p/=2;
    }
    return (int)res;
  }
  static int repow(int b,int p,int modder){
    long a = b%modder;
    long res=1;
    while(p>0){
      if(p%2==1){
        res=(res*a)%modder;
      }
      a=(a*a)%modder;
      p/=2;
    }
    return (int)res;
  }
  static long repow(long b,long p){
    long a = b;
    long res=1;
    while(p>0){
      if(p%2==1){
        res*=a;
      }
      a*=a;
      p/=2;
    }
    return res;
  }
  static long repow(long b,long p,long modder){
    long a = b%modder;
    long res=1;
    while(p>0){
      if(p%2==1){
        res=(res*a)%modder;
      }
      a=(a*a)%modder;
      p/=2;
    }
    return res;
  }
  static long gcd(long c,long d){
    while(true){
      long f=c%d;
      if(f==0){
        return d;
      }
      c=d;
      d=f;
    }
  }
  static long lcm(long c,long d){
    return c/gcd(c,d)*d;
  }
  static ArrayList<Integer> divList(int n){
    ArrayList<Integer> div=new ArrayList<Integer>();
    for(int i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        if(i*i!=n){
          div.add((int)(n/i));
        }
      }
    }
    return div;
  }
  static HashSet<Integer> divSet(int n){
    HashSet<Integer> div=new HashSet<Integer>();
    for(int i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        div.add((int)(n/i));
      }
    }
    return div;
  }
  static Map<Long,Integer> pFacMap(long x){
    Map<Long,Integer> mp=new HashMap<>();
    long t=x;
    for(long i=2;i*i<=x&&i<=t;i++){
      if(t%i==0){
        int num=0;
        while(t%i==0){
          t/=i;
          num++;
        }
        mp.put(i,num);
      }
    }
    if(t!=1){
      mp.put(t,1);
    }
    return mp;
  }
  static boolean iP(long n){
    if(n==2){
      return true;
    }
    if((n&1)==0||n==1){
      return false;
    }
//    if(n>3037007383L){
    if(n>Integer.MAX_VALUE){
      return tameshiwari(n);
    }
    long d=n-1;
    int s=0;
    while((d&1)==0){
      d/=2;
      s++;
    }
    int[] aa = {2,3,5,7,11,13,17};
    for(int i=0;i<7&&aa[i]<n;i++){
      int a = aa[i];
      long t = d;
      long y=repow(a,t,n);
      while(t!=n-1&&y!=1&&y!=n-1){
        y = (y*y)%n;
        t=t<<1;
      }
      if(y!=n-1&&(t&1)==0){
        return false;
      }
    }
    return true;
  }
  static boolean tameshiwari(long n){
    for(long i=2;i*i<=n;i++){
      if(n%i==0){
        return false;
      }
    }
    return true;
  }
  static class NCK{
    int max;
    int mod;
    long[] fac;
    long[] finv;
    long[] inv;
    NCK(){
      this(510000,1000000007);
    }
    NCK(int max,int mod){
      this.max=max;
      this.mod=mod;
      pre(max,mod);
    }
    void pre(int nmax,int nmod){
      fac = new long[nmax];
      finv = new long[nmax];
      inv = new long[nmax];
      fac[0]=fac[1]=1;
      finv[0]=finv[1]=1;
      inv[1]=1;
      for(int i=2;i<nmax;i++){
        fac[i]=fac[i-1]*i%nmod;
        inv[i]=nmod-inv[nmod%i]*(nmod/i)%nmod;
        finv[i]=finv[i-1]*inv[i]%nmod;
      }
    }
    long nCk(int n,int k){
      if(n<k){return 0;}
      if(n<0||k<0){return 0;}
      return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
    }
  }
  static <T extends Comparable<T>> int BSA(List<T> l,T target){
    return BSA(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(List<T> l,T target,Comparator<T> c){
    return BSA(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSA(List<T> l,T target,int left,int right){
    return BSA(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static <T extends Comparable<T>> int BSF(List<T> l,T target){
    return BSF(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(List<T> l,T target,Comparator<T> c){
    return BSF(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSF(List<T> l,T target,int left,int right){
    return BSF(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>=0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSL(List<T> l,T target){
    return BSL(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(List<T> l,T target,Comparator<T> c){
    return BSL(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSL(List<T> l,T target,int left,int right){
    return BSL(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<=0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSA(T[] a,T target){
    return BSA(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(T[] a,T target,Comparator<T> c){
    return BSA(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSA(T[] a,T target,int left,int right){
    return BSA(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static <T extends Comparable<T>> int BSF(T[] a,T target){
    return BSF(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(T[] a,T target,Comparator<T> c){
    return BSF(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSF(T[] a,T target,int left,int right){
    return BSF(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>=0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSL(T[] a,T target){
    return BSL(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(T[] a,T target,Comparator<T> c){
    return BSL(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSL(T[] a,T target,int left,int right){
    return BSL(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<=0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSA(int[] a,int target){
    return BSA(a,target,0,a.length,true);
  }
  static int BSA(int[] a,int target, boolean syojun){
    return BSA(a,target,0,a.length,syojun);
  }
  static int BSA(int[] a,int target,int left,int right){
    return BSA(a,target,left,right,true);
  }
  static int BSA(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static int BSF(int[] a,int target){
    return BSF(a,target,0,a.length,true);
  }
  static int BSF(int[] a,int target,boolean syojun){
    return BSF(a,target,0,a.length,syojun);
  }
  static int BSF(int[] a,int target,int left,int right){
    return BSF(a,target,left,right,true);
  }
  static int BSF(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSL(int[] a,int target){
    return BSL(a,target,0,a.length,true);
  }
  static int BSL(int[] a,int target,boolean syojun){
    return BSL(a,target,0,a.length,syojun);
  }
  static int BSL(int[] a,int target,int left,int right){
    return BSL(a,target,left,right,true);
  }
  static int BSL(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSA(long[] a,long target){
    return BSA(a,target,0,a.length,true);
  }
  static int BSA(long[] a,long target, boolean syojun){
    return BSA(a,target,0,a.length,syojun);
  }
  static int BSA(long[] a,long target,int left,int right){
    return BSA(a,target,left,right,true);
  }
  static int BSA(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static int BSF(long[] a,long target){
    return BSF(a,target,0,a.length,true);
  }
  static int BSF(long[] a,long target,boolean syojun){
    return BSF(a,target,0,a.length,syojun);
  }
  static int BSF(long[] a,long target,int left,int right){
    return BSF(a,target,left,right,true);
  }
  static int BSF(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSL(long[] a,long target){
    return BSL(a,target,0,a.length,true);
  }
  static int BSL(long[] a,long target,boolean syojun){
    return BSL(a,target,0,a.length,syojun);
  }
  static int BSL(long[] a,long target,int left,int right){
    return BSL(a,target,left,right,true);
  }
  static int BSL(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int kmp(String t,String p){
    int[] f=new int[p.length()+1];
    int i=0;
    int j=1;
    f[1]=0;
    while(j<p.length()){
      if(i==0||p.charAt(i-1)==p.charAt(j-1)){
        i++;
        j++;
        f[j]=i;
      }else{
        i=f[i];
      }
    }
    i=1;
    j=1;
    while(i<=p.length()&&j<=t.length()){
      if(i==0||p.charAt(i-1)==t.charAt(j-1)){
        i++;
        j++;
      }else{
        i=f[i];
      }
    }
    return i==(p.length()+1)?j-i:-1;
  }
  static String StSort(String s){
    StringBuilder sb = new StringBuilder(s);
    int lg = sb.length();
    int l;
    int r;
    int gaze;
    for(int i=1;i<lg;i++){
      l=0;
      r=i-1;
      while(l<=r){
        gaze=(l+r)/2;
        if(sb.charAt(gaze)<=sb.charAt(i)){
          l=gaze+1;
        }else if(sb.charAt(gaze)>sb.charAt(i)){
          r=gaze-1;
        }
      }
      sb.insert(l,sb.charAt(i));
      sb.deleteCharAt(i+1);
    }
    return sb.toString();
  }
  static class Xy{
    int x;
    int y;
    Xy(int x,int y){
      this.x=x;
      this.y=y;
    }
    public int manht(Xy o){
      return Math.abs(x-o.x)+Math.abs(y-o.y);
    }
    public String toString(){
      return "["+x+","+y+"]";
    }
    public double henkaku(){
      return Math.atan2(y,x);
    }
    public static int hencom(Xy s1,Xy s2){
      return (int)Math.signum(s1.henkaku()-s2.henkaku());
    }
    public boolean equals(Object o){
      return x==((Xy)o).x&&y==((Xy)o).y;
    }
  }
  static class Zip1{
    Map<Long,Integer> zip=new HashMap<>();
    long[] unzip;
    Zip1(long[] a){
      Arrays.sort(a);
      long mae=0;int zure=0;
      for(int i=0;i<a.length;i++){
        if(i==0||mae!=a[i]){
          zip.put(a[i],i-zure);
          mae=a[i];
        }else{
          zure++;
        }
      }
      unzip=new long[size()];
      for(Map.Entry<Long,Integer> me:zip.entrySet()){
        unzip[me.getValue()]=me.getKey();
      }
    }
    int zip(long t){
      return zip.get(t);
    }
    long unzip(int i){
      return unzip[i];
    }
    int size(){
      return zip.size();
    }
  }
  static class UnFd{
    int n;
    int[] a;
    int[] size;
    int forest;
    UnFd(int n){
      forest=this.n=n;
      a = new int[n];
      size = new int[n];
      for(int i=0;i<n;i++){
        a[i] = i;
        size[i]=1;
      }
    }
    boolean isRoot(int i){
      return a[i]==i;
    }
    int rootOf(int i){
      if(isRoot(i)){
        return i;
      }
      return a[i] = rootOf(a[i]);
    }
    boolean ud(int i,int j){
      return rootOf(i)==rootOf(j);
    }
    boolean marge(int i,int j){
      if(ud(i,j)){
        return false;
      }
      i=rootOf(i);
      j=rootOf(j);
      a[Integer.max(i,j)]=Integer.min(i,j);
      size[j]=size[i]=size[i]+size[j];
      forest-=1;
      return true;
    }
    int sizeOf(int i){
      return size[rootOf(i)];
    }
    int[] roots(){
      int[] rs = new int[forest];
      int p=0;
      for(int i=0;i<n;i++){
        if(isRoot(i)){
          rs[p]=i;
          p++;
        }
      }
      return rs;
    }
  }
  static class SegTree<T>{
    int n;
    int m;
    java.util.function.BinaryOperator<T> op;
    int[] l;
    int[] r;
    T[] a;
    T ident;
    SegTree(int n,java.util.function.BinaryOperator<T> op,T ident){
      this.n=n;
      this.op=op;
      this.ident=ident;
      int ii=n-1;
      int p=0;
      while(ii>0){
        ii/=2;
        p++;
      }
      m=repow(2,p+1)-1;
      @SuppressWarnings("unchecked")
      T[] b=(T[])(new Object[m]);
      a=b;
      Arrays.fill(a,ident);
      l=new int[m];
      r=new int[m];
      for(int i=0;i<=m/2;i++){
        l[m/2+i]=i;
        r[m/2+i]=i+1;
      }
      for(int i=m/2-1;i>=0;i--){
        l[i]=l[lch(i)];
        r[i]=r[rch(i)];
      }
    }
    SegTree(int n,java.util.function.BinaryOperator<T> op,T ident,T[] ary){
      this.n=n;
      this.op=op;
      this.ident=ident;
      int ii=n-1;
      int p=0;
      while(ii>0){
        ii/=2;
        p++;
      }
      m=repow(2,p+1)-1;
      @SuppressWarnings("unchecked")
      T[] b=(T[])(new Object[m]);
      a=b;
      for(int i=0;i<n;i++){
        a[m/2+i]=ary[i];
      }
      for(int i=m/2+n;i<m;i++){
        a[i]=ident;
      }
      for(int i=m/2-1;i>=0;i--){
        a[i]=op.apply(a[lch(i)],a[rch(i)]);
      }
      l=new int[m];
      r=new int[m];
      for(int i=0;i<=m/2;i++){
        l[m/2+i]=i;
        r[m/2+i]=i+1;
      }
      for(int i=m/2-1;i>=0;i--){
        l[i]=l[lch(i)];
        r[i]=r[rch(i)];
      }
    }
    public T getAll(){
      return a[0];
    }
    public T get(int from,int to){
      if(from<0||n<to||from>=to){
        throw new IllegalArgumentException(String.valueOf(from)+","+String.valueOf(to));
      }
      return get(from,to,0);
    }
    private T get(int from,int to,int node){
      if(from==l[node]&&to==r[node]){
        return a[node];
      }else{
        if(to<=l[node]+(r[node]-l[node])/2){
          return get(from,to,lch(node));
        }else if(l[node]+(r[node]-l[node])/2<=from){
          return get(from,to,rch(node));
        }else{
          return op.apply(get(from,l[node]+(r[node]-l[node])/2,lch(node)),get(l[node]+(r[node]-l[node])/2,to,rch(node)));
        }
      }
    }
    public void set(T ob,int i){
      if(i<0||n<=i){
        throw new IndexOutOfBoundsException(String.valueOf(i)+"isOutFromLength "+String.valueOf(n));
      }
      int j=m/2+i;
      a[j]=ob;
      while(true){
        if(j==0){
          break;
        }
        j=prt(j);
        a[j]=op.apply(a[lch(j)],a[rch(j)]);
      }
    }
    static private int prt(int node){
      return (node-1)/2;
    }
    static private int lch(int node){
      return 2*node+1;
    }
    static private int rch(int node){
      return 2*node+2;
    }
    public String toString(){
      return Arrays.toString(a);
    }
  }
  static boolean next_permutation(int[] per){
    if(per.length<2){
      return false;
    }
    int i;
    for(i=per.length-1;i>0;i--){
      if(per[i-1]<per[i]){
        break;
      }
    }
    if(0<i){
      i--;
      int tmp;
      int j;
      for(j=per.length-1;j>i;j--){
        if(per[j]>per[i]){
          break;
        }
      }
      //swap(i,j)
      tmp=per[i];
      per[i]=per[j];
      per[j]=tmp;
      for(int k=i+1;k<(i+1+per.length)/2;k++){
        //swap(k,per.length-k+i)
        tmp=per[k];
        per[k]=per[per.length-k+i];
        per[per.length-k+i]=tmp;
      }
      return true;
    }
    int tmp;
    for(int k=0;k<per.length;k++){
      //swap(k,per.length-k-1)
      tmp=per[k];  
      per[k]=per[per.length-k-1];
      per[per.length-k-1]=tmp;
    }
    return false;
  }
  static boolean next_bits(boolean[] b){
    for(int i=0;i<b.length;i++){
      if(b[i]){
        b[i]=false;
      }else{
        b[i]=true;
        return true;
      }
    }
    return false;
  }
  static class Scnr{
    private final InputStream ins;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    Scnr(){
      this(System.in);
    }
    Scnr(InputStream in){
      ins = in;
    }
    private boolean hasNextByte(){
      if(ptr<buflen){
        return true;
      }else{
        ptr = 0;
        try{
          buflen = ins.read(buffer);
        }catch(IOException e){
          e.printStackTrace();
        }
        if(buflen<=0){
          return false;
        }
      }
      return true;
    }
    private int readByte(){
      if(hasNextByte()){
        return buffer[ptr++];
      }else{
        return -1;
      }
    }
    private static boolean isPrintableChar(int c){
      return 33<=c&&c<=126;
    }
    public boolean hasNext(){
      while(hasNextByte()&&!isPrintableChar(buffer[ptr])){
        ptr++;
      }
      return hasNextByte();
    }
    public String next(){
      return nextBuilder().toString();
    }
    public StringBuilder nextBuilder(){
      if(!hasNext()){
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while(isPrintableChar(b)){
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb;
    }
    public double nextDouble(){
      return Double.parseDouble(next());
    }
    public long nextLong(){
      if(!hasNext()){
        throw new NoSuchElementException();
      }
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if(b=='-'){
        minus=true;
        b=readByte();
      }
      if(b<'0'||'9'<b){
        throw new NumberFormatException();
      }
      while(true){
        if('0'<=b&&b<='9'){
          n*=10;
          n+=b-'0';
        }else if(b==-1||!isPrintableChar(b)){
          return minus?-n:n;
        }else{
          throw new NumberFormatException();
        }
        b=readByte();
      }
    }
    public int nextInt(){
      long nl=nextLong();
      if(nl<Integer.MIN_VALUE||Integer.MAX_VALUE<nl){
        throw new NumberFormatException();
      }
      return (int) nl;
    }
    public String[] nextA(int n){
      String[] a = new String[n];
      nextA(a,n);
      return a;
    }
    public void nextA(String[] a,int n){
      nextA(a,0,n);
    }
    public void nextA(String[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i]=next();
      }
    }
    public int[] nextAInt(int n){
      int[] a = new int[n];
      nextAInt(a,n);
      return a;
    }
    public void nextAInt(int[] a,int n){
      nextAInt(a,0,n);
    }
    public void nextAInt(int[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextInt();
      }
    }
    public long[] nextALong(int n){
      long[] a = new long[n];
      nextALong(a,n);
      return a;
    }
    public void nextALong(long[] a,int n){
      nextALong(a,0,n);
    }
    public void nextALong(long[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextLong();
      }
    }
    public double[] nextADouble(int n){
      double[] a = new double[n];
      nextADouble(a,n);
      return a;
    }
    public void nextADouble(double[] a,int n){
      nextADouble(a,0,n);
    }
    public void nextADouble(double[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextDouble();
      }
    }
    public List<Integer> nextLInt(int n){
      List<Integer> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextInt());
      }
      return l;
    }
    public List<Long> nextLLong(int n){
      List<Long> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextLong());
      }
      return l;
    }
    public List<Double> nextLDouble(int n){
      List<Double> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextDouble());
      }
      return l;
    }
  }
  
  static Scnr sc = new Scnr();
  static PrintWriter out = new PrintWriter(System.out);
  public static void main(String args[]){
    solve();
    out.flush();
  }
  
  static int[] dy={ 0, 1, 0,-1};
  static int[] dx={ 1, 0,-1, 0};
  static char[] dd={'L','U','R','D'};
  static char[] de={'R','D','L','U'};
  static final Xy inf=new Xy(-2,-2);
  
  static void solve(){
    int n=sc.nextInt();
    Set<Xy> bst=new HashSet<>();
    Xy[][] xys=new Xy[n][n];
    for(int i=0;i<n;i++){
      for(int j=0;j<n;j++){
        int y=sc.nextInt()-1;
        int x=sc.nextInt()-1;
        xys[i][j]=new Xy(x,y);
        if(xys[i][j].y==i&&xys[i][j].x==j){
          bst.add(xys[i][j]);
        }
      }
    }
/*
for(int i=0;i<n;i++){
System.err.println(Arrays.toString(xys[i]));
}
*/
    char[][] ans=new char[n][n];
    for(Xy block:bst){
/*
System.err.println("block="+block);
*/
      Deque<Xy> dq=new ArrayDeque<>();
      ans[block.y][block.x]='X';
      dq.addFirst(block);
      while(!dq.isEmpty()){
        Xy here=dq.pollFirst();
/*
System.err.println("  here="+here);
*/
        for(int d=0;d<4;d++){
          int nx=here.x+dx[d];
          int ny=here.y+dy[d];
          if(nx<0||n<=nx||ny<0||n<=ny){
            continue;
          }
          if(ans[ny][nx]==0&&block.equals(xys[ny][nx])){
/*
System.err.println("    d="+d+","+dd[d]);
System.err.println("    ["+nx+","+ny+"]");
*/
            ans[ny][nx]=dd[d];
            dq.add(new Xy(nx,ny));
          }
        }
      }
    }
/*
for(int i=0;i<n;i++){
System.err.println(Arrays.toString(ans[i]));
}
*/
    for(int i=0;i<n;i++){
      for(int j=0;j<n;j++){
        if(ans[i][j]==0){
          if(xys[i][j].equals(inf)){
            for(int d=0;d<4;d++){
              int nx=j+dx[d];
              int ny=i+dy[d];
              if(nx<0||n<=nx||ny<0||n<=ny){
                continue;
              }
              if(xys[ny][nx].equals(inf)){
                ans[i][j]=de[d];
                break;
              }
            }
            if(ans[i][j]==0){
              out.println("INVALID");
              return;
            }
          }else{
            out.println("INVALID");
            return;
          }
        }
      }
    }
/*
for(int i=0;i<n;i++){
System.err.println(Arrays.toString(ans[i]));
}
*/
    out.println("VALID");
    for(int i=0;i<n;i++){
      for(int j=0;j<n;j++){
        out.print(ans[i][j]);
      }
      out.println();
    }
  }
}