Problem: 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.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class codeforces 
{ 
   static class Student{
       int x,y;//z;
        Student(int x,int y){
            this.x=x;
            this.y=y;
            //this.z=z;
        }
    }
    static int prime[];
    static void sieveOfEratosthenes(int n) 
    { 
        // Create a boolean array "prime[0..n]" and initialize 
        // all entries it as true. A value in prime[i] will 
        // finally be false if i is Not a prime, else true. 
        int pos=0;
        prime= new int[n+1]; 
        for(int p = 2; p*p <=n; p++) 
        { 
            // If prime[p] is not changed, then it is a prime 
            if(prime[p] == 0)
            { 
                // Update all multiples of p
                prime[p]=p;
                for(int i = p*p; i <= n; i += p)
                    if(prime[i]==0)
                    prime[i] = p; 
            } 
        } 
    }
static    class Sortbyroll implements Comparator<Student> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(Student c, Student b) 
    {
        return c.x-b.x;
    } 
} 
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            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; 
        } 
    } 
 
    static class Edge{
        int a,b;
        Edge(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    static class Trie{
        HashMap<Character,Trie>map;
         int c;
        Trie(){
            map=new HashMap<>();
            //z=null;
            //o=null;
            c=0;
        }
    }
    //static long ans;
    static int parent[];
    static int rank[];
    static int b[];
    static int bo[];
    static int ho[][];
    static int seg[];
    //static int pos;
    static long mod=1000000000+7;
    //static int dp[][];
    static HashMap<String,Integer>map;
    static PriorityQueue<Student>q=new PriorityQueue<>();
    //static Stack<Integer>st;
   // static ArrayList<Character>ans;
    static ArrayList<ArrayList<Integer>>adj;
    //static ArrayList<ArrayList<Integer>>tr;
    static ArrayList<HashMap<Long,Student>>map1;
    static ArrayList<HashMap<Long,Long>>map2;
    //static long ans;
    static int pos;
    static Trie root;
    static long fac[];
    static int gw,gb;
    //static long mod=(long)(998244353);
    static long ans;
    static void solve()throws IOException{
        FastReader sc=new FastReader();
        int n,k,i,j,x,t_i,s,max,e=0,j1,t_e;
        StringBuilder sb=new StringBuilder();
        n=sc.nextInt();
        int a[]=new int[n];
        for(i=0;i<n;i++){
            a[i]=sc.nextInt();
           // System.out.println(i+" "+a[i]);
        }
        k=sc.nextInt();
        int b[]=new int[k];
        for(i=0;i<k;i++)
            b[i]=sc.nextInt();
        i=0;
        j=0;
        while(j<k&&i<n){
            s=0;
            t_i=i;
            if(a[i]==b[j]){
                //e=i;
                ++i;
                ++j;
                continue;
            }
            while(i<n&&s+a[i]<=b[j]){
                //System.out.println("hello");
                //++i;
                s+=a[i];
                //System.out.println(s);
                ++i;
            }
            //System.out.println(s+" "+"nk");
            i-=1;
            if(s!=b[j]){
                //System.out.println(i+" "+s);
                pos=1;
                break;
            }
            max=0;
            //in=-1;
            for(x=t_i;x<=i;x++){
                max=Math.max(max,a[x]);
            }
            x=t_i;
            while(x<=i){
                if(a[x]==max&&((x-1>=t_i&&a[x-1]!=a[x])||(x+1<=i&&a[x]!=a[x+1])))
                    break;
                ++x;
            }
            if(x>i){
                //System.out.println("kya");
                pos=1;
                break;
            }
            t_e=e;
            if(x-1>=t_i&&a[x-1]!=a[x]){
                sb.append((x+1-e)+" "+"L"+"\n");
                ++t_e;
                for(j1=x+1;j1<=i;j1++){
                    sb.append((x-e)+" "+"R"+"\n");
                    ++t_e;
                }
                for(j1=x-2;j1>=t_i;j1--){
                    sb.append((x-e)+" "+"L"+"\n");
                    ++t_e;
                    --x;
                }
            }
            else{
                sb.append((x+1-e)+" "+"R"+"\n");
                ++t_e;
                for(j1=x+2;j1<=i;j1++){
                    sb.append((x+1-e)+" "+"R"+"\n");
                    ++t_e;
                }//x=x+1;
                for(j1=x-1;j1>=t_i;j1--){
                    sb.append((x+1-e)+" "+"L"+"\n");
                    --x;
                    ++t_e;
                }
            }
            e=t_e;
            //e=i;
            ++i;
            ++j;
        }
        if(pos==1||(i!=n)||j!=k)
            System.out.println("NO");
        else{
            System.out.println("YES");
            System.out.println(sb.toString());
        }
    }

    static void dfs2(int p,int c,long dp1[][],long dp[]){
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs2(c,x,dp1,dp);
            dp[c]=Math.max(dp[c],dp[x]);
            if(dp1[c][0]==Long.MIN_VALUE)
                dp1[c][0]=dp[x];
            else if(dp1[c][0]<=dp[x]){
                dp1[c][1]=dp1[c][0];
                dp1[c][0]=dp[x];
            }
            else
                dp1[c][1]=Math.max(dp1[c][1],dp[x]);
        }
    }
    static void dfs(int p,int c,int a[],long dp[]){
        dp[c]=a[c];
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs(c,x,a,dp);
            dp[c]+=dp[x];
        }
    }
    static void dfs(int x,int y,char f[][],int n,int m){
        f[x][y]='u';
        if(x+1<n){
            if(f[x+1][y]=='*')
                ++pos;
            if(f[x+1][y]=='.')
                dfs(x+1,y,f,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='*')
                ++pos;
            if(f[x-1][y]=='.')
                dfs(x-1,y,f,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='*')
                ++pos;
            if(f[x][y+1]=='.')
                dfs(x,y+1,f,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='*')
                ++pos;
            if(f[x][y-1]=='.')
                dfs(x,y-1,f,n,m);
        }
    }
    static void fill(int x,int y,char f[][],int dp[][],int n,int m){
        dp[x][y]=pos;
        f[x][y]='*';
           if(x+1<n){
            if(f[x+1][y]=='u')
                fill(x+1,y,f,dp,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='u')
                fill(x-1,y,f,dp,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='u')
                fill(x,y+1,f,dp,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='u')
                fill(x,y-1,f,dp,n,m);
        }
    }
    static boolean check(String s){
        int i=0,j=s.length()-1;
        while(i<j){
            if(s.charAt(i)!=s.charAt(j))
                return false;
            ++i;
            --j;
        }
        return true;
    }
    static void update(int s,int e,int l,int r,int in,int v){
        if(s>e||s>r||l>e)
            return;
        if(s>=l&&e<=r){
            seg[in]=v;
            return;
        }
        int mid=(s+e)/2;
        update(s,mid,l,r,2*in+1,v);
        update(mid+1,e,l,r,2*in+2,v);
        seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
        static int query(int s,int e,int l,int r,int in){
        if(s>e||s>r||l>e)
            return 0;
        if(s>=l&&e<=r){
            return seg[in];
            
        }
        int mid=(s+e)/2;
        return Math.max(query(s,mid,l,r,2*in+1),
        query(mid+1,e,l,r,2*in+2));
        //seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
    static double dist(long x,long y,long z,long w){
        return Math.sqrt((x-y)*(x-y)+(z-w)*(z-w));
    }
    static void add(int x,int y,Queue<Integer>q,Queue<Integer>v,int b[][]){
        q.add(x);
        v.add(y);
        b[x][y]=1;
    }
    static long nCr(long n, long r, 
                                    long p) 
    { 
        return (fac[(int)n]* modInverse(fac[(int)r], p) 
                % p * modInverse(fac[(int)(n-r)], p) 
                                    % p) % p; 
    } 
    //static int prime[];
    //static int dp[];
    public static void main(String[] args){
        //long sum=0;
        try {
                codeforces.solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
    }
       static long modInverse(long n, long p) 
    { 
        return power(n, p-(long)2,p); 
    } 
 static long power(long x, long y, long p) 
{ 
    long res = 1;      // Initialize result 
  
    x = x % p;  // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y %(long)2!=0) 
            res = (res*x) % p; 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x) % p;   
    } 
    return res%p;
 }
    /*public static long power(long x,long a) {
		if(a==0) return 1;
		if(a%2==1)return (x*1L*power(x,a-1))%mod;
		return (power((int)((x*1L*x)%mod),a/2))%mod;
	}*/
   static int find(int x) 
    { 
        // Finds the representative of the set 
        // that x is an element of 
        while(parent[x]!=x) 
        { 
            // if x is not the parent of itself 
            // Then x is not the representative of 
            // his set,
            x=parent[x];
  
            // so we recursively call Find on its parent 
            // and move i's node directly under the 
            // representative of this set 
        } 
  
        return x; 
    }
    static void union(int x, int y) 
    { 
        // Find representatives of two sets 
        int xRoot = find(x), yRoot = find(y); 
  
        // Elements are in the same set, no need 
        // to unite anything. 
        if (xRoot == yRoot) 
            return; 
  
         // If x's rank is less than y's rank 
        if (rank[xRoot] < rank[yRoot]) 
  
            // Then move x under y  so that depth 
            // of tree remains less 
            parent[xRoot] = yRoot; 
  
        // Else if y's rank is less than x's rank 
        else if (rank[yRoot] < rank[xRoot]) 
  
            // Then move y under x so that depth of 
            // tree remains less 
            parent[yRoot] = xRoot; 
  
        else // if ranks are the same 
        { 
            // Then move y under x (doesn't matter 
            // which one goes where) 
            parent[yRoot] = xRoot; 
  
            // And increment the the result tree's 
            // rank by 1 
            rank[xRoot] = rank[xRoot] + 1; 
        } 
    } 
    static long gcd(long a, long b) 
    { 
        if (a == 0){ 
             //ans+=b;
            return b;
        }
        return gcd(b % a, a); 
    }
}