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 static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import static java.lang.System.out;
import java.util.*;
import java.io.*;
import java.math.*;
/*
-> Give your 100%, that's it!
-> Rules To Solve Any Problem:
    1. Read the problem.
    2. Think About It.
    3. Solve it!
*/

public class Template {
    
	static int mod = 1000000007;

	public static void main(String[] args){
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int yo = sc.nextInt();
        ot: while (yo-- > 0) {
            int n = sc.nextInt();
            int[] a = new int[n];
            for(int i = 0; i < n; i++){
                a[i] = sc.nextInt();
            }
            char[] c = sc.next().toCharArray();
            
            List<Pair> list = new ArrayList<>();
            for(int i = 0; i < n; i++){
                if(c[i] == 'R'){ // +1
                    if(a[i] > n){
                        out.println("NO");
                        continue ot;
                    }
                    int x = max(a[i],1);
                    int y = n;
                    list.add(new Pair(x,y));
                }
                else { // -1
                    if(a[i] < 1){
                        out.println("NO");
                        continue;
                    }
                    int x = 1;
                    int y = min(a[i],n);
                    list.add(new Pair(x,y));
                }
            }
            
            // Collections.sort(list, (x,y) -> x.y - y.y == 0 ? (int)(x.x-y.x) : (int)(x.y-y.y));
            
            Collections.sort(list, new Comparator<Pair>() {
                @Override
                public int compare(Pair p1, Pair p2) {
                    if(p1.y.compareTo(p2.y) == 0){
                        return p1.x.compareTo(p2.x);
                    }
                    return p1.y.compareTo(p2.y);
                }
            });
            
            for(int i = 0; i < list.size(); i++){
                if(list.get(i).x <= (i+1) && list.get(i).y >= (i+1)){
                    
                }
                else {
                    out.println("NO");
                    continue ot;
                }
            }
            out.println("YES");
        }
        out.close();
	}
    
   
    
    
    /*
    Source: hu_tao
         Random stuff to try when stuck:
            - use bruteforcer
            - always check for n = 1, n = 2, so on
            -if it's 2C then it's dp
            -for combo/probability problems, expand the given form we're interested in
            -make everything the same then build an answer (constructive, make everything 0 then do something)
            -something appears in parts of 2 --> model as graph
            -assume a greedy then try to show why it works
            -find way to simplify into one variable if multiple exist
            -treat it like fmc (note any passing thoughts/algo that could be used so you can revisit them)
            -find lower and upper bounds on answer
            -figure out what ur trying to find and isolate it
            -see what observations you have and come up with more continuations
            -work backwards (in constructive, go from the goal to the start)
            -turn into prefix/suffix sum argument (often works if problem revolves around adjacent array elements)
            -instead of solving for answer, try solving for complement (ex, find n-(min) instead of max)
            -draw something
            -simulate a process
            -dont implement something unless if ur fairly confident its correct
            -after 3 bad submissions move on to next problem if applicable
            -do something instead of nothing and stay organized
            -write stuff down
         Random stuff to check when wa:
            -if code is way too long/cancer then reassess
            -switched N/M
            -int overflow
            -switched variables
            -wrong MOD
            -hardcoded edge case incorrectly
         Random stuff to check when tle:
            -continue instead of break
            -condition in for/while loop bad
         Random stuff to check when rte:
            -switched N/M
            -long to int/int overflow
            -division by 0
            -edge case for empty list/data structure/N=1
      */

	public static class Pair {
		Integer x;
	    Integer y;

		public Pair(Integer x, Integer y) {
			this.x = x;
			this.y = y;
		}
	}

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

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

	static boolean[] sieve(int N) {
		boolean[] sieve = new boolean[N + 1];
		for (int i = 2; i <= N; i++)
			sieve[i] = true;

		for (int i = 2; i <= N; i++) {
			if (sieve[i]) {
				for (int j = 2 * i; j <= N; j += i) {
					sieve[j] = false;
				}
			}
		}
		return sieve;
	}

	public static long power(long x, long y, long p) {
		long res = 1L;
		x = x % p;
		while (y > 0) {
			if ((y & 1) == 1)
				res = (res * x) % p;
			y >>= 1;
			x = (x * x) % p;
		}
		return res;
	}

	public static void print(int[] arr, PrintWriter out) {
		//for debugging only
		for (int x : arr)
			out.print(x + " ");
		out.println();
	}
    
    public static int log2(int a){
        return (int)(Math.log(a)/Math.log(2));
    }

	static class FastScanner {
		private int BS = 1 << 16;
		private char NC = (char) 0;
		private byte[] buf = new byte[BS];
		private int bId = 0, size = 0;
		private char c = NC;
		private double cnt = 1;
		private BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) {
			try {
				in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
			} catch (Exception e) {
				in = new BufferedInputStream(System.in, BS);
			}
		}

		private char getChar() {
			while (bId == size) {
				try {
					size = in.read(buf);
				} catch (Exception e) {
					return NC;
				}
				if (size == -1)
					return NC;
				bId = 0;
			}
			return (char) buf[bId++];
		}

		public int nextInt() {
			return (int) nextLong();
		}

		public int[] readInts(int N) {
			int[] res = new int[N];
			for (int i = 0; i < N; i++) {
				res[i] = (int) nextLong();
			}
			return res;
		}

		public long[] readLongs(int N) {
			long[] res = new long[N];
			for (int i = 0; i < N; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long nextLong() {
			cnt = 1;
			boolean neg = false;
			if (c == NC)
				c = getChar();
			for (; (c < '0' || c > '9'); c = getChar()) {
				if (c == '-')
					neg = true;
			}
			long res = 0;
			for (; c >= '0' && c <= '9'; c = getChar()) {
				res = (res << 3) + (res << 1) + c - '0';
				cnt *= 10;
			}
			return neg ? -res : res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c != '.' ? cur : cur + nextLong() / cnt;
		}

		public double[] readDoubles(int N) {
			double[] res = new double[N];
			for (int i = 0; i < N; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = getChar();
			while (c > 32) {
				res.append(c);
				c = getChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = getChar();
			while (c != '\n') {
				res.append(c);
				c = getChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if (c > 32)
				return true;
			while (true) {
				c = getChar();
				if (c == NC)
					return false;
				else if (c > 32)
					return true;
			}
		}
	}

	//	For Input.txt and Output.txt	
	//	FileInputStream in = new FileInputStream("input.txt");
	//	FileOutputStream out = new FileOutputStream("output.txt");
	//	PrintWriter pw = new PrintWriter(out);
	//	Scanner sc = new Scanner(in);
}