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.*;
import java.util.*;

public final class Main {

    static PrintWriter out = new PrintWriter(System.out);
    static FastReader in = new FastReader();
    static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(0, 1), new Pair(1, 0), new Pair(0, -1)};
    static int mod = (int) (1e9 + 7);
    static int mod2 = 998244353;

    public static void main(String[] args) {
        int tt = i();
        while (tt-- > 0) {
            solve();
        }
        out.flush();
    }

    public static void solve() {
        int n = i();
        int[] a = input(n);
        String c = s();

        List<Integer> b = new ArrayList<>();
        List<Integer> r = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            boolean d = c.charAt(i) == 'B';
            if ((d && a[i] < 0) || (!d && a[i] > n)) {
                out.println("NO");
                return;
            }
            if (d) {
                if (a[i] >= n) {
                } else {
                    b.add(a[i]);
                }
            } else {
                if (a[i] <= 0) {
                } else {
                    r.add(a[i]);
                }
            }
        }
        boolean[] vis = new boolean[n + 1];
        Collections.sort(b);
        Collections.sort(r, (o1, o2) -> o2-o1);
        int i = 1;
        for (int bb : b) {
            while (vis[i]) {
                i++;
            }
            if (bb >= i) {
                vis[i] = true;
                i++;
            } else {
                out.println("NO");
                return;
            }
        }
        i = n;
        for (int rr : r) {
            while (vis[i]) {
                i--;
            }
            if (rr <= i) {
                vis[i] = true;
                i--;
            } else {
                out.println("NO");
                return;
            }
        }
        out.println("YES");
    }

    static long[] pre(int[] a) {
        long[] pre = new long[a.length + 1];
        pre[0] = 0;
        for (int i = 0; i < a.length; i++) {
            pre[i + 1] = pre[i] + a[i];
        }
        return pre;
    }

    static void print(char A[]) {
        for (char c : A) {
            out.print(c);
        }
        out.println();
    }

    static void print(boolean A[]) {
        for (boolean c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(int A[]) {
        for (int c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(long A[]) {
        for (long i : A) {
            out.print(i + " ");
        }
        out.println();
    }

    static void print(List<Integer> A) {
        for (int a : A) {
            out.print(a + " ");
        }
    }

    static int i() {
        return in.nextInt();
    }

    static long l() {
        return in.nextLong();
    }

    static double d() {
        return in.nextDouble();
    }

    static String s() {
        return in.nextLine();
    }

    static int[][] inputWithIdx(int N) {
        int A[][] = new int[N][2];
        for (int i = 0; i < N; i++) {
            A[i] = new int[]{i, in.nextInt()};
        }
        return A;
    }

    static int[] input(int N) {
        int A[] = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N) {
        long A[] = new long[N];
        for (int i = 0; i < A.length; i++) {
            A[i] = in.nextLong();
        }
        return A;
    }

    static int GCD(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

    static long GCD(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

    static long LCM(int a, int b) {
        return (long) a / GCD(a, b) * b;
    }

    static long LCM(long a, long b) {
        return a / GCD(a, b) * b;
    }

    static void shuffleAndSort(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            int temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    static void shuffleAndSort(int[][] arr, Comparator<? super int[]> comparator) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            int[] temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr, comparator);
    }

    static void shuffleAndSort(long[] arr) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            long temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    static boolean isPerfectSquare(double number) {
        double sqrt = Math.sqrt(number);
        return ((sqrt - Math.floor(sqrt)) == 0);
    }

    static void swap(int A[], int a, int b) {
        int t = A[a];
        A[a] = A[b];
        A[b] = t;
    }

    static long pow(long a, long b, int mod) {
        long pow = 1;
        long x = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                pow = (pow * x) % mod;
            }
            x = (x * x) % mod;
            b /= 2;
        }
        return pow;
    }

    static long pow(long a, long b) {
        long pow = 1;
        long x = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                pow *= x;
            }
            x = x * x;
            b /= 2;
        }
        return pow;
    }

    static long modInverse(long x, int mod) {
        return pow(x, mod - 2, mod);
    }

    static boolean isPrime(long N) {
        if (N <= 1) {
            return false;
        }
        if (N <= 3) {
            return true;
        }
        if (N % 2 == 0 || N % 3 == 0) {
            return false;
        }
        for (int i = 5; i * i <= N; i = i + 6) {
            if (N % i == 0 || N % (i + 2) == 0) {
                return false;
            }
        }
        return true;
    }

    public static String reverse(String str) {
        if (str == null) {
            return null;
        }
        return new StringBuilder(str).reverse().toString();
    }

    public static String repeat(char ch, int repeat) {
        if (repeat <= 0) {
            return "";
        }
        final char[] buf = new char[repeat];
        for (int i = repeat - 1; i >= 0; i--) {
            buf[i] = ch;
        }
        return new String(buf);
    }

    public static int[] manacher(String s) {
        char[] chars = s.toCharArray();
        int n = s.length();
        int[] d1 = new int[n];
        for (int i = 0, l = 0, r = -1; i < n; i++) {
            int k = (i > r) ? 1 : Math.min(d1[l + r - i], r - i + 1);
            while (0 <= i - k && i + k < n && chars[i - k] == chars[i + k]) {
                k++;
            }
            d1[i] = k--;
            if (i + k > r) {
                l = i - k;
                r = i + k;
            }
        }
        return d1;
    }

    public static int[] kmp(String s) {
        int n = s.length();
        int[] res = new int[n];
        for (int i = 1; i < n; ++i) {
            int j = res[i - 1];
            while (j > 0 && s.charAt(i) != s.charAt(j)) {
                j = res[j - 1];
            }
            if (s.charAt(i) == s.charAt(j)) {
                ++j;
            }
            res[i] = j;
        }
        return res;
    }
}

class Pair {

    int i, j;

    Pair(int i, int j) {
        this.i = i;
        this.j = j;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) {
            return true;
        }
        if (o == null || getClass() != o.getClass()) {
            return false;
        }
        Pair pair = (Pair) o;
        return i == pair.i && j == pair.j;
    }

    @Override
    public int hashCode() {
        return Objects.hash(i, j);
    }
}

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;
    }
}

class Node {

    int data, open, close;

    Node() {
        this(0, 0, 0);
    }

    Node(int data, int open, int close) {
        this.data = data;
        this.open = open;
        this.close = close;
    }
}

class ST {

    int n;
    Node[] st;

    ST(int n) {
        this.n = n;
        st = new Node[4 * Integer.highestOneBit(n)];
    }

    void build(Node[] nodes) {
        build(0, 0, n - 1, nodes);
    }

    private void build(int id, int l, int r, Node[] nodes) {
        if (l == r) {
            st[id] = nodes[l];
            return;
        }
        int mid = (l + r) >> 1;
        build((id << 1) + 1, l, mid, nodes);
        build((id << 1) + 2, mid + 1, r, nodes);
        st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
    }

    void update(int i, Node node) {
        update(0, 0, n - 1, i, node);
    }

    private void update(int id, int l, int r, int i, Node node) {
        if (i < l || r < i) {
            return;
        }
        if (l == r) {
            st[id] = node;
            return;
        }
        int mid = (l + r) >> 1;
        update((id << 1) + 1, l, mid, i, node);
        update((id << 1) + 2, mid + 1, r, i, node);
        st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
    }

    Node get(int x, int y) {
        return get(0, 0, n - 1, x, y);
    }

    private Node get(int id, int l, int r, int x, int y) {
        if (x > r || y < l) {
            return new Node();
        }
        if (x <= l && r <= y) {
            return st[id];
        }
        int mid = (l + r) >> 1;
        return comb(get((id << 1) + 1, l, mid, x, y), get((id << 1) + 2, mid + 1, r, x, y));
    }

    Node comb(Node a, Node b) {
        if (a == null) {
            return b;
        }
        if (b == null) {
            return a;
        }
        int min = Math.min(a.open, b.close);
        return new Node(a.data + b.data + min * 2, a.open + b.open - min, a.close + b.close - min);
    }
}