There was an epidemic in Monstropolis and all monsters became sick. To recover, all monsters lined up in queue for an appointment to the only doctor in the city.

Soon, monsters became hungry and began to eat each other. 

One monster can eat other monster if its weight is strictly greater than the weight of the monster being eaten, and they stand in the queue next to each other. Monsters eat each other instantly. There are no monsters which are being eaten at the same moment. After the monster A eats the monster B, the weight of the monster A increases by the weight of the eaten monster B. In result of such eating the length of the queue decreases by one, all monsters after the eaten one step forward so that there is no empty places in the queue again. A monster can eat several monsters one after another. Initially there were n monsters in the queue, the i-th of which had weight ai.

For example, if weights are [1, 2, 2, 2, 1, 2] (in order of queue, monsters are numbered from 1 to 6 from left to right) then some of the options are:

  1. the first monster can't eat the second monster because a1 = 1 is not greater than a2 = 2; 
  2. the second monster can't eat the third monster because a2 = 2 is not greater than a3 = 2; 
  3. the second monster can't eat the fifth monster because they are not neighbors; 
  4. the second monster can eat the first monster, the queue will be transformed to [3, 2, 2, 1, 2]. 



After some time, someone said a good joke and all monsters recovered. At that moment there were k (k ≤ n) monsters in the queue, the j-th of which had weight bj. Both sequences (a and b) contain the weights of the monsters in the order from the first to the last.

You are required to provide one of the possible orders of eating monsters which led to the current queue, or to determine that this could not happen. Assume that the doctor didn't make any appointments while monsters were eating each other.

Input

The first line contains single integer n (1 ≤ n ≤ 500) — the number of monsters in the initial queue.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the initial weights of the monsters.

The third line contains single integer k (1 ≤ k ≤ n) — the number of monsters in the queue after the joke. 

The fourth line contains k integers b1, b2, ..., bk (1 ≤ bj ≤ 5·108) — the weights of the monsters after the joke. 

Monsters are listed in the order from the beginning of the queue to the end.

Output

In case if no actions could lead to the final queue, print "NO" (without quotes) in the only line. 

Otherwise print "YES" (without quotes) in the first line. In the next n - k lines print actions in the chronological order. In each line print x — the index number of the monster in the current queue which eats and, separated by space, the symbol 'L' if the monster which stays the x-th in the queue eats the monster in front of him, or 'R' if the monster which stays the x-th in the queue eats the monster behind him. After each eating the queue is enumerated again. 

When one monster eats another the queue decreases. If there are several answers, print any of them.

Examples

Input

6
1 2 2 2 1 2
2
5 5


Output

YES
2 L
1 R
4 L
3 L


Input

5
1 2 3 4 5
1
15


Output

YES
5 L
4 L
3 L
2 L


Input

5
1 1 1 3 3
3
2 1 6


Output

NO

Note

In the first example, initially there were n = 6 monsters, their weights are [1, 2, 2, 2, 1, 2] (in order of queue from the first monster to the last monster). The final queue should be [5, 5]. The following sequence of eatings leads to the final queue:

  * the second monster eats the monster to the left (i.e. the first monster), queue becomes [3, 2, 2, 1, 2]; 
  * the first monster (note, it was the second on the previous step) eats the monster to the right (i.e. the second monster), queue becomes [5, 2, 1, 2]; 
  * the fourth monster eats the mosnter to the left (i.e. the third monster), queue becomes [5, 2, 3]; 
  * the finally, the third monster eats the monster to the left (i.e. the second monster), queue becomes [5, 5]. 



Note that for each step the output contains numbers of the monsters in their current order in the queue.

import java.awt.Point;
import java.awt.geom.Line2D;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileReader;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.security.GuardedObject;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.InputStream;
import java.math.BigInteger;






/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */

public class Main {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
    
        
        OutputStream outputStream = System.out;
        FastScanner in;
        PrintWriter out;
        
           in=new FastScanner(System.in);
            out=new PrintWriter(System.out);
        //in=new FastScanner(new FileInputStream(new File("C://Users//KANDARP//Desktop//coding_contest_creation (1).txt")));
        
        TaskC solver = new TaskC();
        long var=System.currentTimeMillis();
        solver.solve(1, in, out);
        /*if(System.getProperty("ONLINE_JUDGE")==null){
            out.println("["+(double)(System.currentTimeMillis()-var)/1000+"]");
        }*/
        out.close();
    }
}
class Pair {
    
    long x,y,index;
    long  r1,r2;
    
    Pair(long x,long y,int index){
        this.x=x;
        this.y=y;
        this.index=index;
    }
    public String toString(){
        return this.x+" "+this.y+" ";
    }
    
}
class Edge implements  Comparable<Edge>{
    int u;
    int v;
    int time;
    long cost;
    long wcost;
    public Edge(int u,int v,long cost,long wcost){
        this.u=u;
        this.v=v;
        this.cost=cost;
        this.wcost=wcost;
        time=Integer.MAX_VALUE;
    }
    public int other(int x){
        if(u==x)return v;
        return u;
    }
    @Override
    public int compareTo(Edge o) {
        // TODO Auto-generated method stub
        return Long.compare(cost, o.cost);
    }
}
class queary{
    int type;
    int l;
    int r;
    int index;
    queary(int type,int l,int r,int index){
        this.type=type;
        this.l=l;
        this.r=r;
        this.index=index;
    }
}
class TaskC {
    static long mod=1000000007;
   static int prime_len=1000010;
    static int prime[]=new int[prime_len];
    static long n_prime[]=new long[prime_len];
    static ArrayList<Integer> primes=new ArrayList<>();
    static{
        for(int i=2;i<=Math.sqrt(prime.length);i++){
            for(int j=i*i;j<prime.length;j+=i){
                
                prime[j]=i;
                
            }
        }
        for(int i=2;i<prime.length;i++){
            n_prime[i]=n_prime[i-1];
            if(prime[i]==0){
               n_prime[i]++;
            }
            
        }
    //  System.out.println("end");
        
    //  prime[0]=true;
    //  prime[1]=1;
    }
    /*
     *  long pp[]=new long[10000001];
            pp[0]=0;
            pp[1]=1;
            for(int i=2;i<pp.length;i++){
                if(prime[i]!=0){
                    int gcd=(int)greatestCommonDivisor(i/prime[i], prime[i]);
                    pp[i]=(pp[i/prime[i]]*pp[prime[i]]*gcd)/pp[(int)gcd];
                }
                else
                    pp[i]=i-1;
            }
        

}
     * */
    
    class TrieNode{
        int value;
        TrieNode children[];
        public TrieNode(int value,TrieNode children[] ){
            this.value=value;
            this.children=children;
        }
    }
    class Trie{
        TrieNode root;
        int count;
        public Trie(TrieNode root,int count){
            this.root=root;
            this.count=count;
        }
    }
    public void insert(Trie t,char key[]){
        t.count++;
        int length=key.length;
        int level=0;
        TrieNode current=t.root;
        if(current==null){
            t.root=new TrieNode(0, new TrieNode[26]);
            current=t.root;
        }
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                current.children[index]=new TrieNode(0,new TrieNode[26]);
            }
            current=current.children[index];
        }
        current.value=t.count;
    }
    public int search(Trie t,char key[]){
        TrieNode current=t.root;
        if(current==null){
            return 0;
        }
        int length=key.length;
        int level=0;
        for(level=0;level<length;level++){
            int index=key[level]-'a';
            if(current.children[index]==null){
                return 0;
            }
            current=current.children[index];
        }
        return current.value;
    }
    class point implements Comparable<point>{
        long x;
        long y;
        public point(long x,long y){
            this.x=x;
            this.y=y;
        }
        @Override
        public int compareTo(point o) {
            // TODO Auto-generated method stub
            if(o.x==x && o.y==y)
            return 0;
            else return (int)Math.max(x-o.x, y-o.y);
        }
        public int hashCode(){
            return (int)(x+y);
            
        }
        public boolean equals(Object z){
            if(z!=null){
                point o=(point)z;
                if(o.x==x && o.y==y)
                    return true;
            }
            return false;
        }
        
    }
    class Edge {
        int t, rev, cap, f;

        public Edge(int t, int rev, int cap) {
          this.t = t;
          this.rev = rev;
          this.cap = cap;
        }
      }

    class MaxFlowDinic {

          
          public  List<Edge>[] createGraph(int nodes) {
            List<Edge>[] graph = new List[nodes];
            for (int i = 0; i < nodes; i++)
              graph[i] = new ArrayList<>();
            return graph;
          }

          public  void addEdge(List<Edge>[] graph, int s, int t, int cap) {
            graph[s].add(new Edge(t, graph[t].size(), cap));
            graph[t].add(new Edge(s, graph[s].size() - 1, 0));
          }

           boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
            Arrays.fill(dist, -1);
            dist[src] = 0;
            int[] Q = new int[graph.length];
            int sizeQ = 0;
            Q[sizeQ++] = src;
            for (int i = 0; i < sizeQ; i++) {
              int u = Q[i];
              for (Edge e : graph[u]) {
                if (dist[e.t] < 0 && e.f < e.cap) {
                  dist[e.t] = dist[u] + 1;
                  Q[sizeQ++] = e.t;
                }
              }
            }
            return dist[dest] >= 0;
          }

           int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
            if (u == dest)
              return f;
            for (; ptr[u] < graph[u].size(); ++ptr[u]) {
              Edge e = graph[u].get(ptr[u]);
              if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
                int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
                if (df > 0) {
                  e.f += df;
                  graph[e.t].get(e.rev).f -= df;
                  return df;
                }
              }
            }
            return 0;
          }

          public  int maxFlow(List<Edge>[] graph, int src, int dest) {
            int flow = 0;
            int[] dist = new int[graph.length];
            while (dinicBfs(graph, src, dest, dist)) {
              int[] ptr = new int[graph.length];
              while (true) {
                int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
                if (df == 0)
                  break;
                flow += df;
              }
            }
            return flow;
          }
    }
        //int arr[]=new int[1000000000];
    int n,k,a[],b[];
    
    public void solve(int testNumber, FastScanner in, PrintWriter out) throws IOException {
    	n=in.nextInt();
    	a=new int[n];
    	
    	for(int i=0;i<n;i++){
    		a[i]=in.nextInt();
    	}
    	 k=in.nextInt();
    	 b=new int[k];
    	for(int i=0;i<k;i++){
    		b[i]=in.nextInt();
    	}
    	StringBuilder sb=fun(0,0);
    	if(sb==null){
    		out.println("NO");
    	}
    	else{
    		out.println("YES");
    		out.println(sb);
    	}
    
    }
    public StringBuilder fun(int i,int j){
    	//System.out.println(i+" "+j);
    	if(i>=n && j>=k){
    		return new StringBuilder();
    	}
    	if(i>=n){
    		return null;
    	}
    	if(j>=k){
    		return null;
    	}
    	int x=b[j];
    	int sum=0;
    	int max=0;
    	int index=0;
    	int rec=-1;
    	for(int l=i;l<n;l++){
    		sum+=a[l];
    		int tmp=max;
    		max=Math.max(max,a[l]);
    		if(max!=tmp){
    			index=l;
    		}
    		if(max==a[l]){
    			if(l-1>=i && a[l]>a[l-1]){
    				index=l;
    			}
    			
    		}
    		if(sum==x){
    			rec=l;
    			break;
    		}
    		if(max==a[l] && l+1<n && a[l]>a[l+1]){
				index=l;
			}
    		
    	}
    	if(rec==-1){
    		return null;
    	}
    	StringBuilder sb=fun(rec+1,j+1);
    	if(sb==null){
    		return null;
    	}
    	//System.out.println(index);
    	StringBuilder ans=new StringBuilder();
    	boolean xx=false;
    	int ts=a[index];
    	for(int l=index-1;l>=i;l--){
    		int aa= (l+1-(i)+j);
    		if(a[l]==ts){
    		//	System.out.println(l+" "+index);
    			xx=true;
    			break;
    		}
    		ts+=a[l];
    		ans.append((aa+1)+" L\n");
    	}
    	//System.out.println(xx);
    	ts=a[index];
    	for(int l=index+1;l<=rec;l++){
    		//System.out.println(l+" "+index);
    		if((a[l]==ts && xx) || (a[l]==ts && index==i)){
    			return null;
    		}
    		if(!xx)
    		ans.append((j+1)+" R\n");
    		else
    			ans.append((index-i+j+1)+" R\n");
    		
    		ts+=a[l];
    	}
    	
    	if(xx){
    		
    		for(int l=index-1;l>=i;l--){
        		int aa= (l+1-(i)+j);
        		if(a[l]==ts){
        			return null;
        			
        		}
        		ans.append((aa+1)+" L\n");
        	}
    	}
    	ans.append(sb);
    return ans;
    }
   
        
    public long[] fun(long n,int k,int a){
        long arr[]=new long[k];
        for(int i=0;i<k;i++){
            
            arr[(int)(pow(i, a, k)%k)]+=((n/k)%mod+ ((i!=0  &&  i<=n%k)? 1: 0))%mod;
        }
        return arr;
    }
         
     
     public long getAns(int d[],int n){
         if(d[0]<0 && d[n-1]>0){
             
             return Math.min(-2*d[0]+d[n-1], 2*d[n-1]-d[0]);
             
             
          }
          else{
              if(d[0]<0){
                     return d[0]*-1;
              }
              else{
                     return(d[n-1]*1);
              }
          }
         
        // return 0;
     }
     public boolean isTriangle(int x,int y,int z){
         if(x+y>z && x+z>y && y+z>x){
             return true;
         }
         return false;
     }
     public long optimize(long x){
         long y=x;
         if(x%10<5){
             x=x-x%10;
            
         }
         else{
             x=x+(10-x%10);
         }
         return y-x;
     }
   public static long[][] matrixexpo(long m[][],String n,long mod){
       if(n.equals("1")){
           return m.clone();
       }
       if(n.equals("10")){
           return mulmatrix(m, m , mod);
       }
       else{
           long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
           temp=mulmatrix(temp, temp, mod);
           if(n.charAt(n.length()-1)=='0')return temp;
           else return mulmatrix(temp, m,mod);
       }
   }
   
    public static long[] mul(long[] a, long[] b)
    {
        int n = Math.max(a.length, b.length);
        int h = Integer.highestOneBit(n);
        if(n > h)h *= 2;
        if(a.length < h)a = Arrays.copyOf(a, h);
        if(b.length < h)b = Arrays.copyOf(b, h);
        return mul2(a, b, 0, h, 0, h);
    }
    
    public static long[] mul2(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar-al;
        if((n&n-1) != 0)throw new RuntimeException();
        if(n <= 1<<6){
            long[] res = muln(a, b, al, ar, bl, br);
            return res;
        }
        
        long[] c0 = mul2(a, b, al+0, al+n/2, bl+0, bl+n/2);
        long[] c2 = mul2(a, b, al+n/2, al+n, bl+n/2, bl+n);
        
        long[] ab0 = new long[n/2];
        long[] ab1 = new long[n/2];
        for(int i = 0;i < n/2;i++){
            ab0[i] = a[al+i] + a[al+i+n/2];
            ab1[i] = b[bl+i] + b[bl+i+n/2];
            if(ab0[i] >= mod)ab0[i] -= mod;
            if(ab1[i] >= mod)ab1[i] -= mod;
        }
        
        int e = n+c2.length;
        long[] ret = new long[e];
        for(int i = 0;i < c0.length;i++){
            ret[i] += c0[i];
            if(ret[i] >= mod)ret[i] -= mod;
        }
        for(int i = 0;i < c2.length;i++){
            ret[i+n] += c2[i];
            if(ret[i+n] >= mod)ret[i+n] -= mod;
        }
        
        long[] c1 = mul2(ab0, ab1, 0, n/2, 0, n/2);
        for(int i = 0;i < c1.length;i++){
            c1[i] -= c0[i] + c2[i];
            if(c1[i] < 0)c1[i] += mod;
            if(c1[i] < 0)c1[i] += mod;
        }
        for(int i = 0;i < c1.length;i++){
            ret[i+n/2] += c1[i];
            if(ret[i+n/2] >= mod)ret[i+n/2] -= mod;
        }
        return ret;
    }
    
    public static long[] muln(long[] a, long[] b, int al, int ar, int bl, int br)
    {
        int n = ar - al;
        long[] ret = new long[2*n];
        for(int i = 0;i < 2*n;i++){
            long tot = 0;
            for(int j = Math.max(i-n+1, 0);j <= i && j < n;j++){
                tot += a[al+j] * b[bl+i-j];
            }
            ret[i] = tot % mod;
        }
        return ret;
    }
    
   public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
       long ans[][]=new long[m1.length][m2[0].length];
       for(int i=0;i<m1.length;i++){
           for(int j=0;j<m2[0].length;j++){
               for(int k=0;k<m1.length;k++){
                   ans[i][j]+=(m1[i][k]*m2[k][j]);
                   ans[i][j]%=mod;
               }
           }
       }
       return ans;
   }
   long pow(long x,long y,long mod){
       if(y<=0){
           return 1;
       }
       if(y==1){
           return x%mod;
       }
       long temp=pow(x,y/2,mod);
       if(y%2==0){
           return (temp*temp)%mod;
       }
       else{
           return (((temp*temp)%mod)*x)%mod;
       }
   }    
        
   
    

   static long greatestCommonDivisor (long m, long n){
       long x;
       long y;
       while(m%n != 0){
           x = n;
           y = m%n;
           m = x;
           n = y;
       }
       return n;
   }
   static void dfs(List<Integer>[] graph, boolean[] used, List<Integer> res, int u,int parent,List<Integer> collection) {
       
       used[u] = true;
       Integer uu=new Integer(u);
       collection.add(uu);
       for (int v : graph[u]){
         if (!used[v]){
           dfs(graph, used, res, v,u,collection);
           
         }
         else if(collection.contains(v)){
             System.out.println("Impossible");
             System.exit(0);
         }
       }
       collection.remove(uu);
       res.add(u);
     }
   
       
     public static List<Integer> topologicalSort(List<Integer>[] graph) {
       int n = graph.length;
       boolean[] used = new boolean[n];
       List<Integer> res = new ArrayList<>();
       for (int i = 0; i < n; i++)
         if (!used[i])
           dfs(graph, used, res, i,-1,new ArrayList<Integer>());
       Collections.reverse(res);
       return res;
     }     
     
 }
    





     
 
    class LcaSparseTable {

          int len;
          int[][] up;
          int[][] max;
          int[] tin;
          int[] tout;
          int time;
          int []lvel;
          
          void dfs(List<Integer>[] tree, int u, int p) {
            tin[u] = time++;
            lvel[u]=lvel[p]+1;
            up[0][u] = p;
            if(u!=p)
            //max[0][u]=weight(u,p);
            for (int i = 1; i < len; i++)
              {
                up[i][u] = up[i - 1][up[i - 1][u]];
                max[i][u]=Math.max(max[i-1][u],max[i-1][up[i-1][u]]);
              }
            for (int v : tree[u])
              if (v != p)
                dfs(tree, v, u);
            tout[u] = time++;
          }

          public LcaSparseTable(List<Integer>[] tree, int root) {
            int n = tree.length;
            len = 1;
            while ((1 << len) <= n) ++len;
            up = new int[len][n];
            max=new int[len][n];
            tin = new int[n];
            tout = new int[n];
            lvel=new int[n];
            lvel[root]=0;
            dfs(tree, root, root);
          }

          boolean isParent(int parent, int child) {
            return tin[parent] <= tin[child] && tout[child] <= tout[parent];
          }

          public int lca(int a, int b) {
            if (isParent(a, b))
              return a;
            if (isParent(b, a))
              return b;
            for (int i = len - 1; i >= 0; i--)
              if (!isParent(up[i][a], b))
                a = up[i][a];
            return up[0][a];
          }
          public long max(int a,int b){
              int lca=lca(a,b);
        //    System.out.println("LCA "+lca);
              long ans=0;
              int h=lvel[a]-lvel[lca];
            //  System.out.println("Height "+h);
              int index=0;
              while(h!=0){
                  if(h%2==1){
                      ans=Math.max(ans,max[index][a]);
                      a=up[index][a];
                  }
                  h/=2;
                  index++;
              }
              h=lvel[b]-lvel[lca];
             // System.out.println("Height "+h);
              
              index=0;
              while(h!=0){
                  if(h%2==1){
                      ans=Math.max(ans,max[index][b]);
                      b=up[index][b];
                  }
                  h/=2;
                  index++;
              }
              return ans;
          }
          
    
        
            static void dfs1(List<Integer>[] graph, boolean[] used, List<Integer> res, int u) {
            used[u] = true;
            for (int v : graph[u])
              if (!used[v])
                dfs1(graph, used, res, v);
            res.add(u);
          }

        
        int phi(int n) {
            int res = n;
            for (int i = 2; i * i <= n; ++i) {
                if (n % i == 0) {
                    while (n % i == 0) {
                        n /= i;
                    }
                    res -= res / i;
                }
            }
            if (n != 1) {
                res -= res / n;
            }
            return res;
        }
        
        
        
        public static long[][] mulmatrix(long m1[][],long m2[][],long mod){
            long ans[][]=new long[m1.length][m2[0].length];
            for(int i=0;i<m1.length;i++){
                for(int j=0;j<m2[0].length;j++){
                    for(int k=0;k<m1.length;k++){
                        ans[i][j]+=(m1[i][k]*m2[k][j]);
                        ans[i][j]%=mod;
                    }
                }
            }
            return ans;
        }
        public static long[][] matrixexpo(long m[][],String n,long mod){
            if(n.equals("1")){
                return m.clone();
            }
            if(n.equals("10")){
                return mulmatrix(m, m , mod);
            }
            else{
                long temp [][]=matrixexpo(m,n.substring(0,n.length()-1),mod);
                temp=mulmatrix(temp, temp, mod);
                if(n.charAt(n.length()-1)=='0')return temp;
                else return mulmatrix(temp, m,mod);
            }
        }
        public static boolean isCompatible(long x[],long y[]){
            
            for(int i=0;i<x.length-1;i++){
                if(x[i]==y[i] && x[i+1]==y[i+1] && x[i]==x[i+1] && y[i]==y[i+1]){
                    return false;
                }
            }
            return true;
        }
        
        
        long pow(long x,long y,long mod){
            if(y<=0){
                return 1;
            }
            if(y==1){
                return x%mod;
            }
            long temp=pow(x,y/2,mod);
            if(y%2==0){
                return (temp*temp)%mod;
            }
            else{
                return (((temp*temp)%mod)*x)%mod;
            }
        }
     
        
                long no_of_primes(long m,long n,long k){
                    long count=0,i,j;
                    int primes []=new int[(int)(n-m+2)];
                       if(m==1)    primes[0] = 1;
                        for(i=2; i<=Math.sqrt(n); i++)
                        {
                            j = (m/i);    j *= i;
                            if(j<m)
                                j+=i;
                            for(; j<=n; j+=i)
                             {
                                 if(j!=i)
                                    primes[(int)(j-m)] = 1;
                             }
                        }

                for(i=0; i<=n-m; i++)
                            if(primes[(int)i]==0 && (i-1)%k==0)
                                count++;
                return count;
                }
                
}
    
class SegTree {
    int n;
    static long constt=Long.parseLong("111111111111111111111111111111",2);
    long  t[];
    long mod=(long)(1000000007);
    SegTree(int n,long  t[]){
        this.n=n;
        this.t=t;
        build();
    }
    
    void build() {  // build the tree
        
        for (int i = n - 1; i >= 0; --i){
            t[i]=(t[i<<1]&t[i<<1|1]);
          }
    }

     void modify(int p, long value) {  // set value at position p
      for (t[p += n]=value; p > 1; p >>= 1) t[p>>1] = (t[p]&t[p^1]);
    //  System.out.println(Arrays.toString(t));
     }

     long query(int l, int r) {  // sum on interval [l, r)
         long res=constt;
         
         for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
               if ((l&1)!=0) res=res&t[l++];
               if ((r&1)!=0) res=res&t[--r];
             }
         return res;
      
      
     }

    
    //  
//  
//  
}
class FastScanner
{

    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar;
    private int snumChars;
    private SpaceCharFilter filter;

    public FastScanner(InputStream stream) {
        this.stream = stream;
    }
    
    public int snext() {
        if (snumChars == -1)
            throw new InputMismatchException();
        if (curChar >= snumChars) {
            curChar = 0;
            try {
                snumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (snumChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    public int nextInt() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = snext();
        }

        int res = 0;

        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = snext();
        } while (!isSpaceChar(c));

        return res * sgn;
    }
    
    public long nextLong() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = snext();
        }

        long res = 0;

        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = snext();
        } while (!isSpaceChar(c));

        return res * sgn;
    }
    
    public String readString() {
        int c = snext();
        while (isSpaceChar(c))
            c = snext();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = snext();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}
 class UF {

    private int[] parent;  // parent[i] = parent of i
    private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
    private int count;     // number of components
    public UF(int N) {
        if (N < 0) throw new IllegalArgumentException();
        count = N;
        parent = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) {
            parent[i] = i;
            rank[i] = 0;
        }
    }

    public int find(int p) {
        if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
        while (p != parent[p]) {
            parent[p] = parent[parent[p]];    // path compression by halving
            p = parent[p];
        }
        return p;
    }
    public int count() {
        return count;
    }

    public boolean connected(int p, int q) {
        return find(p) == find(q);
    }

    public boolean union(int p, int q) {
        int rootP = find(p);
        int rootQ = find(q);
        if (rootP == rootQ) return false;

        // make root of smaller rank point to root of larger rank
        if      (rank[rootP] < rank[rootQ]) parent[rootP] = rootQ;
        else if (rank[rootP] > rank[rootQ]) parent[rootQ] = rootP;
        else {
            parent[rootQ] = rootP;
            rank[rootP]++;
        }
        count--;
        return true;
    }
    



}
 class MyScanner {
       BufferedReader br;
       StringTokenizer st;
      
       public MyScanner() {
          br = new BufferedReader(new InputStreamReader(System.in));
       }
      
       String next() {
          while (st == null || !st.hasMoreElements()) {
             try {
                st = new StringTokenizer(br.readLine());
             } catch (IOException e) {
                e.printStackTrace();
             }
          }
          return st.nextToken();
       }
      
       int nextInt() {
          return Integer.parseInt(next());
       }
      
       long nextLong() {
          return Long.parseLong(next());
       }
      
       double nextDouble() {
          return Double.parseDouble(next());
       }
      
       String nextLine(){
          String str = "";
          try {
             str = br.readLine();
          } catch (IOException e) {
             e.printStackTrace();
          }
          return str;
       }
    
    }
	
