You are given an array of integers a of length n. The elements of the array can be either different or the same. 

Each element of the array is colored either blue or red. There are no unpainted elements in the array. One of the two operations described below can be applied to an array in a single step:

  * either you can select any blue element and decrease its value by 1; 
  * or you can select any red element and increase its value by 1. 



Situations in which there are no elements of some color at all are also possible. For example, if the whole array is colored blue or red, one of the operations becomes unavailable.

Determine whether it is possible to make 0 or more steps such that the resulting array is a permutation of numbers from 1 to n?

In other words, check whether there exists a sequence of steps (possibly empty) such that after applying it, the array a contains in some order all numbers from 1 to n (inclusive), each exactly once.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of input data sets in the test.

The description of each set of input data consists of three lines. The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the original array a. The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the array elements themselves.

The third line has length n and consists exclusively of the letters 'B' and/or 'R': ith character is 'B' if a_i is colored blue, and is 'R' if colored red.

It is guaranteed that the sum of n over all input sets does not exceed 2 ⋅ 10^5.

Output

Print t lines, each of which contains the answer to the corresponding test case of the input. Print YES as an answer if the corresponding array can be transformed into a permutation, and NO otherwise.

You can print the answer in any case (for example, the strings yEs, yes, Yes, and YES will be recognized as a positive answer).

Example

Input


8
4
1 2 5 2
BRBR
2
1 1
BB
5
3 1 4 2 5
RBRRB
5
3 1 3 1 3
RBRRB
5
5 1 5 1 5
RBRRB
4
2 2 2 2
BRBR
2
1 -2
BR
4
-2 -1 4 0
RRRR


Output


YES
NO
YES
YES
NO
YES
YES
YES

Note

In the first test case of the example, the following sequence of moves can be performed:

  * choose i=3, element a_3=5 is blue, so we decrease it, we get a=[1,2,4,2]; 
  * choose i=2, element a_2=2 is red, so we increase it, we get a=[1,3,4,2]; 
  * choose i=3, element a_3=4 is blue, so we decrease it, we get a=[1,3,3,2]; 
  * choose i=2, element a_2=2 is red, so we increase it, we get a=[1,4,3,2]. 



We got that a is a permutation. Hence the answer is YES.
    import java.io.BufferedReader;
    import java.io.FileInputStream;
    import java.io.FileNotFoundException;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.util.*;
import java.util.concurrent.LinkedBlockingDeque;
import java.io.PrintStream;
    import java.io.PrintWriter;
    import java.io.DataInputStream;

        public class Solution {

            //TEMPLATE -------------------------------------------------------------------------------------

            public static boolean Local(){
                try{ 
                    return System.getenv("LOCAL_SYS")!=null;
                }catch(Exception e){
                    return false;
                }
            }   

            public static boolean LOCAL;

            static class FastScanner {

                    BufferedReader br;
                    StringTokenizer st ;

                    FastScanner(){
                        br =  new BufferedReader(new InputStreamReader(System.in));
                        st = new StringTokenizer("");
                    }

                    FastScanner(String file) {

                        try{
                            br =  new BufferedReader(new InputStreamReader(new FileInputStream(file)));
                            st = new StringTokenizer("");
                        }catch(FileNotFoundException e) {
                            // TODO Auto-generated catch block
                            System.out.println("file not found");
                            e.printStackTrace();
                        }
                        
                    }
                    String next() {
                        while (!st.hasMoreTokens())
                            try {
                                st = new StringTokenizer(br.readLine());
                            } catch (IOException e) {
                            }
                        return st.nextToken();
                    }
                    int nextInt() {
                        return Integer.parseInt(next());
                    }
                    long nextLong() {
                        return Long.parseLong(next());
                    }
                    String readLine() throws IOException{
                        return br.readLine();
                    }
                }
                                    
            static class Pair<T,X> {

                T first;
                X second;
                
                Pair(T first,X second){
                    this.first = first;
                    this.second = second;
                }

                @Override
                public int hashCode(){
                    return Objects.hash(first,second);
                }

                @Override
                public boolean equals(Object obj){
                    return obj.hashCode() == this.hashCode();
                }

            }

        
        static PrintStream debug = null;
        
        
        static long mod = (long)(Math.pow(10,9) + 7); 
       //TEMPLATE -------------------------------------------------------------------------------------END//
        public static void main(String[] args) throws Exception {
            
            FastScanner s = new FastScanner();
            LOCAL = Local();
            //PrintWriter pw = new PrintWriter(System.out);
            if(LOCAL){
                s = new FastScanner("src/input.txt");
                PrintStream o = new PrintStream("src/sampleout.txt");
                debug = new PrintStream("src/debug.txt");
                System.setOut(o);
            //  pw = new PrintWriter(o);
            } long mod = 1000000007;

        
            int tcr = s.nextInt();                  
            
            StringBuilder sb = new StringBuilder();

            for(int tc=0;tc<tcr;tc++){
                TreeMap<Integer,Integer> red = new TreeMap<>();
                TreeMap<Integer,Integer> blue = new TreeMap<>();
                int n = s.nextInt();
                int arr[] = new int[n];
                for(int i=0;i<n;i++){
                    arr[i] = s.nextInt();
                }
                String str = s.next();
                
                for(int i=0;i<str.length();i++){
                    if(str.charAt(i) == 'B'){
                        blue.put(arr[i],blue.getOrDefault(arr[i],0) + 1);
                    }else{
                        red.put(arr[i],red.getOrDefault(arr[i],0) + 1);
                    }
                }
                boolean poss = true;
                for(int i=n;i>=1;i--){
                    Integer jst_gt_b = blue.ceilingKey(i);
                    Integer jst_sm_r = red.floorKey(i);
                    if(jst_gt_b == null && jst_sm_r == null){poss = false;break;}
                    
                    if(jst_sm_r != null){
                        dec(red,jst_sm_r);
                    }else{
                        dec(blue,jst_gt_b);
                    }
                
                }
                if(poss){
                    sb.append("YES\n");
                }else{
                    sb.append("NO\n");
                }

            }    


            print(sb.toString());
        }

        public static void dec(TreeMap<Integer,Integer> map,int n){
            int cnt = map.get(n);
            if(cnt == 1){map.remove(n);return;}
            map.put(n,cnt - 1);
        }
 
        

        public static List<int[]> print_prime_factors(int n){
        
            List<int[]> list = new ArrayList<>();
            
            for(int i=2;i<=(int)(Math.sqrt(n));i++){
    
                if(n % i == 0){
                    
                    int cnt = 0;
                    
                    while( (n % i) == 0){
                        n = n/i;
                        cnt++;
                    }
    
                    list.add(new int[]{i,cnt});
                }
            }
    
            if(n!=1){
                list.add(new int[]{n,1});
            }

            return list;
        }

        public static List<int[]> prime_factors(int n,List<Integer> sieve){
            List<int[]> list = new ArrayList<>();
            int index = 0;
            while(n > 1 && sieve.get(index) <= Math.sqrt(n)){
                int curr = sieve.get(index);
                int cnt = 0;
                while((n % curr) == 0){
                    n = n/curr;
                    cnt++;
                }
                if(cnt >= 1){
                    list.add(new int[]{curr,cnt});
                }
                index++;
            }
            if(n > 1){
                list.add(new int[]{n,1});
            }
            return list;
        }

        public static boolean inRange(int r1,int r2,int val){
            return ((val >= r1) && (val <= r2));
        }

        static int len(long num){
            return Long.toString(num).length();
        }

        static long mulmod(long a, long b,long mod)
        {
            long ans = 0l;
            
            while(b > 0){
                long curr = (b & 1l);
                if(curr == 1l){
                    ans = ((ans % mod) + a) % mod;
                }
                
                a = (a + a) % mod;

                b = b >> 1;
            }

            return ans;
        }


        public static void dbg(PrintStream ps,Object... o) throws Exception{
            if(ps == null){
                return;
            }
            Debug.dbg(ps,o);
        }

        public static long modpow(long num,long pow,long mod){

            long val = num;
            long ans = 1l;

            while(pow > 0l){
                
                long bit = pow & 1l;

                if(bit == 1){
                    ans = (ans * (val%mod))%mod;
                }

                val = (val * val) % mod;
                pow = pow >> 1;
            }

            return ans;

        }

        public static char get(int n){
            return (char)('a' + n);
        }

        public static long[] sort(long arr[]){
            List<Long> list = new ArrayList<>();
            for(long n : arr){list.add(n);}
            Collections.sort(list);
            for(int i=0;i<arr.length;i++){
                arr[i] = list.get(i);
            }
            return arr;
        }

        public static int[] sort(int arr[]){
            List<Integer> list = new ArrayList<>();
            for(int n : arr){list.add(n);}
            Collections.sort(list);
            for(int i=0;i<arr.length;i++){
                arr[i] = list.get(i);
            }
            return arr;
        }

        // return the (index + 1)
        // where index is the pos of just smaller element
        // i.e count of elemets strictly less than num
        public static int justSmaller(long arr[],long num){
            //  System.out.println(num+"@");
            int st = 0;
            int e = arr.length - 1;

            int ans = -1;

            while(st <= e){

                int mid = (st + e)/2;

                if(arr[mid] >= num){
                    e = mid - 1;
                }else{
                    ans = mid;
                    st = mid + 1;
                }

            }


            return ans + 1;

        }
        public static int justSmaller(int arr[],int num){
            //  System.out.println(num+"@");
            int st = 0;
            int e = arr.length - 1;

            int ans = -1;

            while(st <= e){

                int mid = (st + e)/2;

                if(arr[mid] >= num){
                    e = mid - 1;
                }else{
                    ans = mid;
                    st = mid + 1;
                }

            }


            return ans + 1;

        }
        
        //return (index of just greater element)
        //count of elements smaller than or equal to num

        public static int justGreater(long arr[],long num){
            int st = 0;
            int e = arr.length - 1;

            int ans = arr.length;

            while(st <= e){
                
                int mid = (st + e)/2;

                if(arr[mid] <= num){
                    st = mid + 1;
                }else{
                    ans = mid;
                    e = mid - 1;
                }
            }

            return ans;

        }

        public static int justGreater(int arr[],int num){
            int st = 0;
            int e = arr.length - 1;

            int ans = arr.length;

            while(st <= e){
                
                int mid = (st + e)/2;

                if(arr[mid] <= num){
                    st = mid + 1;
                }else{
                    ans = mid;
                    e = mid - 1;
                }
            }

            return ans;

        }

        

        public static void println(Object obj){
            System.out.println(obj.toString());
        }

        public static void print(Object obj){
            System.out.print(obj.toString());
        }

        public static int gcd(int a,int b){
            if(b == 0){return a;}
            return gcd(b,a%b);
        }

        public static long gcd(long a,long b){
            if(b == 0l){
                return a;
            }

            return gcd(b,a%b);
        }

        public static int find(int parent[],int v){
            if(parent[v] == v){
                return v;
            }
            
            return parent[v] = find(parent, parent[v]);
        }



        public static List<Integer> sieve(){
        
                List<Integer> prime = new ArrayList<>();

                int arr[] = new int[100001];

            Arrays.fill(arr,1);

            arr[1] = 0;
            arr[2] = 1;

            for(int i=2;i<=100000;i++){
                
                if(arr[i] == 1){
                    
                    prime.add(i);

                    for(long j = (i*1l*i);j<100001;j+=i){
                        arr[(int)j] = 0;
                    }
                }
            }

            return prime;
        }

        static boolean isPower(long n,long a){
            
            long log = (long)(Math.log(n)/Math.log(a));

            long power = (long)Math.pow(a,log);

            if(power == n){return true;}

            return false;
        }


        private static int mergeAndCount(int[] arr, int l,int m, int r)
        {
            // Left subarray
            int[] left =  Arrays.copyOfRange(arr, l, m + 1);

            // Right subarray
            int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);

            int i = 0, j = 0, k = l, swaps = 0;

            while (i < left.length && j < right.length) {
                if (left[i] <= right[j])
                    arr[k++] = left[i++];
                else {
                    arr[k++] = right[j++];
                    swaps += (m + 1) - (l + i);
                }
            }
            while (i < left.length)
                arr[k++] = left[i++];
            while (j < right.length)
                arr[k++] = right[j++];
            return swaps;
        }

        // Merge sort function
        private static int mergeSortAndCount(int[] arr, int l,int r)
        {

            // Keeps track of the inversion count at a
            // particular node of the recursion tree
            int count = 0;

            if (l < r) {
                int m = (l + r) / 2;

                // Total inversion count = left subarray count
                // + right subarray count + merge count

                // Left subarray count
                count += mergeSortAndCount(arr, l, m);

                // Right subarray count
                count += mergeSortAndCount(arr, m + 1, r);

                // Merge count
                count += mergeAndCount(arr, l, m, r);
            }

            return count;
        }

        static class Debug{
            //change to System.getProperty("ONLINE_JUDGE")==null; for CodeForces
            public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

            

            private static <T> String ts(T t) {
                if(t==null) {
                    return "null";
                }
                try {
                    return ts((Iterable) t);
                }catch(ClassCastException e) {
                    if(t instanceof int[]) {
                        String s = Arrays.toString((int[]) t);
                        return "{"+s.substring(1, s.length()-1)+"}\n";
                    }else if(t instanceof long[]) {
                        String s = Arrays.toString((long[]) t);
                        return "{"+s.substring(1, s.length()-1)+"}\n";
                    }else if(t instanceof char[]) {
                        String s = Arrays.toString((char[]) t);
                        return "{"+s.substring(1, s.length()-1)+"}\n";
                    }else if(t instanceof double[]) {
                        String s = Arrays.toString((double[]) t);
                        return "{"+s.substring(1, s.length()-1)+"}\n";
                    }else if(t instanceof boolean[]) {
                        String s = Arrays.toString((boolean[]) t);
                        return "{"+s.substring(1, s.length()-1)+"}\n";
                    }
                    try {
                        return ts((Object[]) t);
                    }catch(ClassCastException e1) {
                        return t.toString();
                    }
                }
            }
            private static <T> String ts(T[] arr) {
                StringBuilder ret = new StringBuilder();
                ret.append("{");
                boolean first = true;
                for(T t: arr) {
                    if(!first) {
                        ret.append(", ");
                    }
                    first = false;
                    ret.append(ts(t));
                }
                ret.append("}");
                return ret.toString();
            }
            private static <T> String ts(Iterable<T> iter) {
                StringBuilder ret = new StringBuilder();
                ret.append("{");
                boolean first = true;
                for(T t: iter) {
                    if(!first) {
                        ret.append(", ");
                    }
                    first = false;
                    ret.append(ts(t));
                }
                ret.append("}\n");
                return ret.toString();
            }
            public static void dbg(PrintStream ps,Object... o) throws Exception {
                if(LOCAL) {
                    System.setErr(ps);
                    System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [\n");
                    for(int i = 0; i<o.length; i++) {
                        if(i!=0) {
                            System.err.print(", ");
                        }
                        System.err.print(ts(o[i]));
                    }
                    System.err.println("]");
                }
            }
        }

    }