Problem: Ashish has n elements arranged in a line. 

These elements are represented by two integers a_i — the value of the element and b_i — the type of the element (there are only two possible types: 0 and 1). He wants to sort the elements in non-decreasing values of a_i.

He can perform the following operation any number of times: 

  * Select any two elements i and j such that b_i ≠ b_j and swap them. That is, he can only swap two elements of different types in one move. 



Tell him if he can sort the elements in non-decreasing values of a_i after performing any number of operations.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The first line of each test case contains one integer n (1 ≤ n ≤ 500) — the size of the arrays.

The second line contains n integers a_i (1 ≤ a_i ≤ 10^5) — the value of the i-th element.

The third line containts n integers b_i (b_i ∈ \{0, 1\}) — the type of the i-th element.

Output

For each test case, print "Yes" or "No" (without quotes) depending on whether it is possible to sort elements in non-decreasing order of their value.

You may print each letter in any case (upper or lower).

Example

Input


5
4
10 20 20 30
0 1 0 1
3
3 1 2
0 1 1
4
2 2 4 8
1 1 1 1
3
5 15 4
0 0 0
4
20 10 100 50
1 0 0 1


Output


Yes
Yes
Yes
No
Yes

Note

For the first case: The elements are already in sorted order.

For the second case: Ashish may first swap elements at positions 1 and 2, then swap elements at positions 2 and 3.

For the third case: The elements are already in sorted order.

For the fourth case: No swap operations may be performed as there is no pair of elements i and j such that b_i ≠ b_j. The elements cannot be sorted.

For the fifth case: Ashish may swap elements at positions 3 and 4, then elements at positions 1 and 2.

Solution (in JAVA):

Solution:

import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;

public class Main {
    public static void main(String[] args) throws Exception {
        ScanReader in = new ScanReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solver main = new Solver();
        int test = in.scanInt();
        for (int i = 1; i <= test; i++) main.solve(i, in, out);
        out.close();
    }
}

class Solver {
    public void solve(int testNumber, ScanReader in, PrintWriter out) throws IOException {
        int n = in.scanInt();
        int[][] ar = new int[n][2];
        int[] type = new int[2];
        boolean sorted = true;
        int last = -1;
        for (int[] a : ar) a[0] = in.scanInt();
        for (int[] a : ar) a[1] = in.scanInt();
        for (int[] a : ar) {
            type[a[1]]++;
            if (a[0] < last) sorted = false;
            last = a[0];
        }
        if (sorted) {
            out.println("Yes");
        } else if (type[0] != 0 && type[1] != 0) {
            out.println("Yes");
        } else {
            out.println("No");
        }

    }
}


class ScanReader {
    private final byte[] buf = new byte[4 * 1024];
    private final BufferedInputStream in;
    private int index;
    private int total;

    public ScanReader(InputStream inputStream) {
        in = new BufferedInputStream(inputStream);
    }

    private int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) return -1;
        }
        return buf[index++];
    }

    public char scanChar() throws IOException {
        int c = scan();
        while (isWhiteSpace(c)) c = scan();
        return (char) c;
    }


    public int scanInt() throws IOException {
        int integer = 0;
        int n = scan();
        while (isWhiteSpace(n)) n = scan();
        int neg = 1;
        if (n == '-') {
            neg = -1;
            n = scan();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = scan();
            }
        }
        return neg * integer;
    }

    public String scanString() throws IOException {
        int c = scan();
        while (isWhiteSpace(c)) c = scan();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = scan();
        } while (!isWhiteSpace(c));
        return res.toString();
    }

    private boolean isWhiteSpace(int n) {
        return n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1;
    }

    public long scanLong() throws IOException {
        long integer = 0;
        int n = scan();
        while (isWhiteSpace(n)) n = scan();
        int neg = 1;
        if (n == '-') {
            neg = -1;
            n = scan();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = scan();
            }
        }
        return neg * integer;
    }

    public void scanLong(long[] A) throws IOException {
        for (int i = 0; i < A.length; i++) A[i] = scanLong();
    }

    public void scanInt(int[] A) throws IOException {
        for (int i = 0; i < A.length; i++) A[i] = scanInt();
    }

    public double scanDouble() throws IOException {
        int c = scan();
        while (isWhiteSpace(c)) c = scan();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = scan();
        }
        double res = 0;
        while (!isWhiteSpace(c) && c != '.') {
            if (c == 'e' || c == 'E') {
                return res * Math.pow(10, scanInt());
            }
            res *= 10;
            res += c - '0';
            c = scan();
        }
        if (c == '.') {
            c = scan();
            double m = 1;
            while (!isWhiteSpace(c)) {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, scanInt());
                }
                m /= 10;
                res += (c - '0') * m;
                c = scan();
            }
        }
        return res * sgn;
    }

}