BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. 

You can choose m — the number of screens and s — the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:

  * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); 
  * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). 



Your task is to find the minimal possible number of screens m.

Input

The first line contains an integer t (1 ≤ t ≤ 10 000) — the number of test cases in the input. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2⋅10^6) — the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ n), where c_i is the category of the i-th application.

It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2⋅10^6.

Output

Print t integers — the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m — the minimum number of screens on which all n icons can be placed satisfying the given requirements.

Example

Input


3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2


Output


3
3
4

Note

In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
import java.io.*;
import java.util.*;
import java.math.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class JustArrangeTheIcons {
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(in.nextInt(), in, out);
        out.close();
    }
    static class TaskA {
        long mod = (long)(1000000007);
        public void solve(int testNumber, InputReader in, PrintWriter out) throws IOException {
            while(testNumber-->0){
            	int n = in.nextInt();
            	HashMap<Integer , Integer> m = new HashMap<>();
            	for(int i=0;i<n;i++)
            		mapAdd(m , in.nextInt() , 1);
            	ArrayList<Integer> a = new ArrayList<>();
            	for(int i:m.keySet())
            		a.add(m.get(i));
            	Collections.sort(a);
            	long ans = 0;
            	for(int i = a.get(0)+1;i>=2;i--){
            		long count = 0;
            		boolean ok = true;
            		for(int j=0;j<a.size() && ok;j++){
            			int value = a.get(j);
            			int min = (int)Math.ceil((float)(-value)/(i-1));
            			int max = (int)Math.floor((float)(-value)/(i));
            			if(max>=min){
            				count += value + max*(i-1);
            				count += (-value - max*i); 
            			}
            			else
            				ok = false;
            		}
            		if(ok){
            			ans = count;
            			break;
            		}
            	}
            	out.println(ans);
            }
        }
        public void mapAdd(HashMap<Integer , Integer> m , Integer x , Integer y){
        	if(!m.containsKey(x))
        		m.put(x , 0);
        	m.put(x , m.get(x) + y);
        }
        public void update(long a[] , int index , long value){
        	for(int i=index;i<a.length;i += i&(-i))
        		a[i] += value;
        }
        public long get(long a[] , int index){
        	long res = 0;
        	for(int i=index;i>0;i-=i&(-i))
        		res += a[i];
        	return res;
        }
        public int[] nextGreater(int a[] , int n){
        	int ng[] = new int[n+1];
            Deque<Combine> s = new LinkedList<>();
            for(int i=n;i>0;i--){
                int k = i;
                Combine c = new Combine(a[k] , k);
                while(s.size()>0 && s.peekLast().value <= c.value){
                    Combine d = s.pollLast();
                    ng[d.delete] = c.delete;
                }
                s.addLast(c);
            }
            return ng;
        }
        public void sieve(int a[]){
            a[0] = a[1] = 1;
            int i;
            for(i=2;i*i<=a.length;i++){
                if(a[i] != 0)
                    continue;
                a[i] = i;
                for(int k = (i)*(i);k<a.length;k+=i){
                    if(a[k] != 0)
                        continue;
                    a[k] = i;
                }
            }
        }
        public int [][] matrixExpo(int c[][] , int n){
            int a[][] = new int[c.length][c[0].length];
            int b[][] = new int[a.length][a[0].length];
            for(int i=0;i<c.length;i++)
                for(int j=0;j<c[0].length;j++)
                    a[i][j] = c[i][j];
            for(int i=0;i<a.length;i++)
                b[i][i] = 1;
            while(n!=1){
                if(n%2 == 1){
                    b = matrixMultiply(a , a);
                    n--;
                }
                a = matrixMultiply(a , a);
                n/=2;
            }
            return matrixMultiply(a , b);
        }
        public int [][] matrixMultiply(int a[][] , int b[][]){
            int r1 = a.length;
            int c1 = a[0].length;
            int c2 = b[0].length;
            int c[][] = new int[r1][c2];
            for(int i=0;i<r1;i++){
                for(int j=0;j<c2;j++){
                    for(int k=0;k<c1;k++)
                        c[i][j] += a[i][k]*b[k][j];
                }
            }
            return c;
        }
        public long nCrPFermet(int n , int r , long p){
            if(r==0)
                return 1l;
            long fact[] = new long[n+1];
            fact[0] = 1;
            for(int i=1;i<=n;i++)
                fact[i] = (i*fact[i-1])%p;
            long modInverseR = pow(fact[r] , p-2 , 1l , p);
            long modInverseNR = pow(fact[n-r] , p-2 , 1l , p);
            long w = (((fact[n]*modInverseR)%p)*modInverseNR)%p;
            return w;
        }
        public long pow(long a , long b , long res , long mod){
            if(b==0)
                return res;
            if(b==1)
                return (res*a)%mod;
            if(b%2==1){
                res *= a;
                res %= mod;
                b--;
            }
            // System.out.println(a + " " + b + " " + res);
            return pow((a*a)%mod , b/2 , res , mod);
        }
        public long pow(long a , long b , long res){
            if(b == 0)
                return res;
            if(b==1)
                return res*a;
            if(b%2==1){
                res *= a;
                b--;
            }
            return pow(a*a , b/2 , res);
        }
        public void swap(int a[] , int p1 , int p2){
            int x = a[p1];
            a[p1] = a[p2];
            a[p2] = x;
        }
        public void sortedArrayToBST(TreeSet<Integer> a , int start, int end) { 
            if (start > end) {
                return;
            }
            int mid = (start + end) / 2;
            a.add(mid);
            sortedArrayToBST(a, start, mid - 1);
            sortedArrayToBST(a, mid + 1, end); 
        }
        class Combine{
            int value;
            int delete;
            Combine(int val , int delete){
                this.value = val;
                this.delete = delete;
            }
        }
        class Sort2 implements Comparator<Combine>{
            public int compare(Combine a , Combine b){
                if(a.value > b.value)
                    return 1;
                else if(a.value == b.value && a.delete>b.delete)
                    return 1;
                else if(a.value == b.value && a.delete == b.delete)
                    return 0;
                return -1;
            }
        }
        public int lowerLastBound(ArrayList<Integer> a , int x){
            int l = 0;
            int r = a.size()-1;
            if(a.get(l)>=x)
                return -1;
            if(a.get(r)<x)
                return r;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a.get(mid) == x && a.get(mid-1)<x)
                    return mid-1;
                else if(a.get(mid)>=x)
                    r = mid-1;
                else if(a.get(mid)<x && a.get(mid+1)>=x)
                    return mid;
                else if(a.get(mid)<x && a.get(mid+1)<x)
                    l = mid+1;
            }
            return mid;
        }
        public int upperFirstBound(ArrayList<Integer> a , Integer x){
            int l = 0;
            int r = a.size()-1;
            if(a.get(l)>x)
                return l;
            if(a.get(r)<=x)
                return r+1;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a.get(mid) == x && a.get(mid+1)>x)
                    return mid+1;
                else if(a.get(mid)<=x)
                    l = mid+1;
                else if(a.get(mid)>x && a.get(mid-1)<=x)
                    return mid;
                else if(a.get(mid)>x && a.get(mid-1)>x)
                    r = mid-1;
            }
            return mid;
        }
        public int lowerLastBound(int a[] , int x){
            int l = 0;
            int r = a.length-1;
            if(a[l]>=x)
                return -1;
            if(a[r]<x)
                return r;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a[mid] == x && a[mid-1]<x)
                    return mid-1;
                else if(a[mid]>=x)
                    r = mid-1;
                else if(a[mid]<x && a[mid+1]>=x)
                    return mid;
                else if(a[mid]<x && a[mid+1]<x)
                    l = mid+1;
            }
            return mid;
        }
        public int upperFirstBound(long a[] , long x){
            int l = 0;
            int r = a.length-1;
            if(a[l]>x)
                return l;
            if(a[r]<=x)
                return r+1;
            int mid = -1;
            while(l<=r){
                mid = (l+r)/2;
                if(a[mid] == x && a[mid+1]>x)
                    return mid+1;
                else if(a[mid]<=x)
                    l = mid+1;
                else if(a[mid]>x && a[mid-1]<=x)
                    return mid;
                else if(a[mid]>x && a[mid-1]>x)
                    r = mid-1;
            }
            return mid;
        }
        public long log(float number , int base){
            return (long) Math.floor((Math.log(number) / Math.log(base)));
        }
        public long gcd(long a , long b){
            if(a<b){
                long c = b;
                b = a;
                a = c;
            }
            if(b == 0)
                return a;
            return gcd(b , a%b);
        }
        public void print2d(long a[][] , PrintWriter out){
            for(int i=0;i<a.length;i++){
                for(int j=0;j<a[i].length;j++)
                    out.print(a[i][j] + " ");
                out.println();
            }
            out.println();
        }
        public void print1d(int a[] , PrintWriter out){
            for(int i=0;i<a.length;i++)
                out.print(a[i] + " ");
            out.println();
            out.println();
        }
        class Node{
        	int index;
        	Node right;
        	Node left;
        	public Node(int index){
        		this.index = index;
        		right = null;
        		left = null;
        	}
        }
        class AVLTree{
            Node root;
            public AVLTree(){
                this.root = null;
            }
            public int height(Node n){
                return (n == null ? 0 : n.height);
            }
            public int getBalance(Node n){
                return (n == null ? 0 : height(n.left) - height(n.right));
            }
            public Node rotateRight(Node a){
                Node b = a.left;
                Node br = b.right;

                a.lSum -= b.lSum;
                a.lCount -= b.lCount;
                
                b.rSum += a.rSum;
                b.rCount += a.rCount;
                
                b.right = a;
                a.left = br;
                
                a.height = 1 + Math.max(height(a.left) , height(a.right));
                b.height = 1 + Math.max(height(b.left) , height(b.right));
                return b;
            }
            public Node rotateLeft(Node a){
                Node b = a.right;
                Node bl = b.left;
                
                a.rSum -= b.rSum;
                a.rCount -= b.rCount;
                
                b.lSum += a.lSum;
                b.lCount += a.lCount;
                
                b.left = a;
                a.right = bl;
                
                a.height = 1 + Math.max(height(a.left) , height(a.right));
                b.height = 1 + Math.max(height(b.left) , height(b.right));
                return b;
            }
            public Node insert(Node root , long value){
                if(root == null){
                    return new Node(value);
                }
                if(value<=root.value){
                    root.lCount++;
                    root.lSum += value;
                    root.left =  insert(root.left , value);
                }
                if(value>root.value){
                    root.rCount++;
                    root.rSum += value;
                    root.right = insert(root.right , value);
                }
                // updating the height of the root
                root.height = 1 + Math.max(height(root.left) , height(root.right));
                int balance = getBalance(root);

                //ll
                if(balance>1 && value<=root.left.value)
                    return rotateRight(root);
                //rr
                if(balance<-1 && value>root.right.value)
                    return rotateLeft(root);
                //lr
                if(balance>1 && value>root.left.value){
                    root.left = rotateLeft(root.left);
                    return rotateRight(root);
                }
                //rl
                if(balance<-1 && value<=root.right.value){
                    root.right = rotateRight(root.right);
                    return rotateLeft(root);
                }
                return root;
            }
            public void insertElement(long value){
                this.root = insert(root , value);
            }
            public int getElementLessThanK(long k){
                int count = 0;
                Node temp = root;
                while(temp!=null){
                    if(temp.value == k){
                        if(temp.left == null || temp.left.value<k){
                            count += temp.lCount;
                            return count-1;
                        }
                        else
                            temp = temp.left;
                    }
                    else if(temp.value>k){
                        temp = temp.left;
                    }
                    else{
                        count += temp.lCount;
                        temp = temp.right;
                    }
                }
                return count;
            }
            public void inorder(Node root , PrintWriter out){
                Node temp = root;
                if(temp!=null){
                    inorder(temp.left , out);
                    out.println(temp.value + " " + temp.lCount + " " + temp.rCount);
                    inorder(temp.right , out);
                }
            }
            class Node{
	            long value;
	            long lCount , rCount;
	            long lSum , rSum;
	            Node left , right;
	            int height;
	            public Node(long value){
	                this.value = value;
	                left = null;
	                right = null;
	                lCount = 1;
	                rCount = 1;
	                lSum = value;
	                rSum = value;
	                height = 1;
	            }
	        }
        }
        
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}
