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.util.*;
import java.lang.*;
import java.io.*;

public class Codeforces {
    static FastReader sc=new FastReader();
	static long mod=1000000007;
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		PrintWriter out=new PrintWriter(System.out);
		StringBuffer sb=new StringBuffer();
		int t=I();
		outer:while(t-->0)
		{
			int n=I();
			int a[]=new int[n];
			for(int i=0;i<n;i++){
				a[i]=I();
			}
			int b[]=new int[n];
			int zero=0,one=0;
			for(int i=0;i<n;i++){
				b[i]=I();
				if(b[i]==0)zero++;
				else one++;
			}
			int cor=0;
			for(int i=1;i<n;i++){
				if(a[i]>=a[i-1]){
					cor++;
				}
			}
			if(cor==n-1)sb.append("YES\n");
			else if(zero==0 || one==0)sb.append("NO\n");
			else sb.append("YES\n");
		}
		out.print(sb.toString());
		out.close();
	}
	public static void DFS(ArrayList<Integer> arr[],int s,boolean visited[])
	{
		visited[s]=true;
		for(int i:arr[s]){
			if(!visited[i]){
				DFS(arr,i,visited);
			}
		}
	}
	public static int BS(long a[],long x,int ii,int jj)
	{
		// int n=a.length;
		int mid=0;
		int i=ii,j=jj;
		while(i<=j)
		{
			mid=(i+j)/2;
			if(a[mid]>x)
			j=mid-1;
			else if(a[mid]<=x)
			i=mid+1;
		}
		if(a[mid]>x && mid>ii)
		return mid-1;
		else
		return mid;
	}
	public static ArrayList<Integer> prime(int n)
	{
	    ArrayList<Integer> arr=new ArrayList<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}
	public static HashSet<Integer> primeSet(int n)
	{
	    HashSet<Integer> arr=new HashSet<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}

	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
	public static class FenwickTree
	{
		long farr[];
		int n;
		public FenwickTree(int c)
		{
			n=c+1;
			farr=new long[n];
		}
		public void update_range(int l,int r,long p)
		{
			update(l,p);
			update(r+1,(-1)*p);
		}
		public void update(int x,long p)
		{
			for(;x<n;x+=x&(-x))
			{
				farr[x]+=p;
			}
		}
		public long get(int x)
		{
			long ans=0;
			for(;x>0;x-=x&(-x))
			{
				ans=ans+farr[x];
			}
			return ans;
		}
	}

	//Disjoint Set Union
	public static class DSU
	{
	    static int par[],rank[];
	    public DSU(int c)
	    {
	        par=new int[c+1];
	        rank=new int[c+1];
	        for(int i=0;i<=c;i++)
	        {
	            par[i]=i;
	            rank[i]=0;
	        }
	    }
	    public static int find(int a)
	    {
	        if(a==par[a])
	        return a;
	        return par[a]=find(par[a]);
	    }
	    public static void union(int a,int b)
	    {
	        int a_rep=find(a),b_rep=find(b);
	        if(a_rep==b_rep)
	        return;
	        if(rank[a_rep]<rank[b_rep])
	        par[a_rep]=b_rep;
	        else if(rank[a_rep]>rank[b_rep])
	        par[b_rep]=a_rep;
	        else
	        {
	            par[b_rep]=a_rep;
	            rank[a_rep]++;
	        }
	    }
	}

	//SEGMENT TREE CODE

	// public static void segmentUpdate(int si,int ss,int se,int qs,int qe,long x)
	// {
	// 	if(ss>qe || se<qs)return;
	// 	if(qs<=ss && qe>=se)
	// 	{
	// 		seg[si][0]+=1L;
	// 		seg[si][1]+=x*x;
	// 		seg[si][2]+=2*x;
	// 		return;
	// 	}
	// 	int mid=(ss+se)/2;
	// 	segmentUpdate(2*si+1,ss,mid,qs,qe,x);
	// 	segmentUpdate(2*si+2,mid+1,se,qs,qe,x);
	// }
	// public static long segmentGet(int si,int ss,int se,int x,long f,long s,long t,long a[])
	// {
	// 	if(ss==se && ss==x)
	// 	{
	// 		f+=seg[si][0];
	// 		s+=seg[si][1];
	// 		t+=seg[si][2];
	// 		long ans=a[x]+(f*((long)x+1L)*((long)x+1L))+s+(t*((long)x+1L));
	// 		return ans;
	// 	}
	// 	int mid=(ss+se)/2;
	// 	if(x>mid){
	// 		return segmentGet(2*si+2,mid+1,se,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
	// 	}else{
	// 		return segmentGet(2*si+1,ss,mid,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
	// 	}
	// }

	public static class pair
    {
    	int a;
    	int b;
    	public pair(int val,int index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
	public static class myComp implements Comparator<pair>
	{
		//sort in ascending order.
		public int compare(pair p1,pair p2)
		{
			if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
		}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
	}
    public static class myComp1 implements Comparator<pair1>
    {
		//sort in ascending order.
    	public int compare(pair1 p1,pair1 p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
    	}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
    }
	public static class pair1
    {
    	long a;
    	long b;
    	public pair1(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
    public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
	{
	    //****************use this in main function-Collections.sort(arr,new myComp1());
	    ArrayList<pair1> a1=new ArrayList<>();
	    if(arr.size()<=1)
	    return arr;
	    a1.add(arr.get(0));
	    int i=1,j=0;
	    while(i<arr.size())
	    {
	        if(a1.get(j).b<arr.get(i).a)
	        {
	           a1.add(arr.get(i));
	           i++;
	           j++;
	        }
	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
	        {
	            i++;
	        }
	        else if(a1.get(j).b>=arr.get(i).a)
	        {
	            long a=a1.get(j).a;
	            long b=arr.get(i).b;
	            a1.remove(j);
	            a1.add(new pair1(a,b));
	            i++;
	        }
	    }
	    return a1;
	}
	public static boolean palindrome(String s,int n)
	{
		for(int i=0;i<=n/2;i++){
			if(s.charAt(i)!=s.charAt(n-i-1)){
				return false;
			}
		}
		return true;
	}
	public static long countDigit(long n)
	{
	    long sum=0;
	    while(n!=0)
	    {
	        sum++;
	        n=n/10;
	    }
	    return sum;
	}
	public static long digitSum(long n)
	{
	    long sum=0;
	    while(n!=0)
	    {
	        sum=sum+n%10;
	        n=n/10;
	    }
	    return sum;
	}
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static int gcd(int a,int b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long pwr(long m,long n)
	{
		long res=1;
		m=m%mod;
		if(m==0)
		return 0;
		while(n>0)
		{
			if((n&1)!=0)
			{
				res=(res*m)%mod;
			}
			n=n>>1;
			m=(m*m)%mod;
		}
		return res;
	}
	public static void sort(int[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
    public static void sort(long[] A)
	{
	    int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
	    Arrays.sort(A);
	}
    public static int I(){return sc.I();}
    public static long L(){return sc.L();}
    public static String S(){return sc.S();}
    public static double D(){return sc.D();}
}
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 I(){ 
        return Integer.parseInt(next());
    }
    long L(){ 
        return Long.parseLong(next());
    }
    double D(){
         return Double.parseDouble(next());
    }
    String S(){
        String str = "";
        try 
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}