This problem is a version of problem D from the same contest with some additional constraints and tasks.

There are n candies in a candy box. The type of the i-th candy is a_i (1 ≤ a_i ≤ n). 

You have to prepare a gift using some of these candies with the following restriction: the numbers of candies of each type presented in a gift should be all distinct (i. e. for example, a gift having two candies of type 1 and two candies of type 2 is bad).

It is possible that multiple types of candies are completely absent from the gift. It is also possible that not all candies of some types will be taken to a gift.

You really like some of the candies and don't want to include them into the gift, but you want to eat them yourself instead. For each candy, a number f_i is given, which is equal to 0 if you really want to keep i-th candy for yourself, or 1 if you don't mind including it into your gift. It is possible that two candies of the same type have different values of f_i.

You want your gift to be as large as possible, but you don't want to include too many of the candies you want to eat into the gift. So, you want to calculate the maximum possible number of candies that can be included into a gift, and among all ways to choose maximum number of candies, you want to maximize the number of candies having f_i = 1 in your gift.

You have to answer q independent queries.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

The first line of each query contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of candies.

Then n lines follow, each containing two integers a_i and f_i (1 ≤ a_i ≤ n, 0 ≤ f_i ≤ 1), where a_i is the type of the i-th candy, and f_i denotes whether you want to keep the i-th candy for yourself (0 if you want to keep it, 1 if you don't mind giving it away).

It is guaranteed that the sum of n over all queries does not exceed 2 ⋅ 10^5.

Output

For each query print two integers:

  * the maximum number of candies in a gift you can compose, according to the constraints in the statement; 
  * the maximum number of candies having f_i = 1 in a gift you can compose that contains the maximum possible number of candies. 

Example

Input


3
8
1 0
4 1
2 0
4 1
5 1
6 1
3 0
2 0
4
1 1
1 1
2 1
2 1
9
2 0
2 0
4 1
4 1
4 1
7 0
7 1
7 0
7 1


Output


3 3
3 3
9 5

Note

In the first query, you can include two candies of type 4 and one candy of type 5. All of them have f_i = 1 and you don't mind giving them away as part of the gift.
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		InputReader in = new InputReader(inputStream);
		
//		for(int i=4;i<=4;i++) {
//			InputStream uinputStream = new FileInputStream("leftout.in");
//			String f = i+".in";
//			InputStream uinputStream = new FileInputStream(f);
//			InputReader in = new InputReader(uinputStream);
//			PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("leftout.out")));
			Task t = new Task();
			t.solve(in, out);
			out.close();			
//		}
	}	
	
	static class Task {
		int times = 0;
		public void solve(InputReader in, PrintWriter out) throws IOException {
//			//int xxx = in.nextInt();
//			//while(xxx-->0) {
//				int n = in.nextInt();
//				int k = in.nextInt();
//				int a[] = in.readIntArray(n);
//				int b[] = in.readIntArray(n);
//				ArrayList<Integer>[] g = new ArrayList[n];
//				for(int i=0;i<n;i++) g[i] = new ArrayList<Integer>();
//				for(int i=0;i<n-1;i++) {
//					g[a[i]-1].add(a[i+1]-1);
//					g[b[i]-1].add(b[i+1]-1);
//				}
//				boolean vis[] = new boolean[n];
//				int lvl[] = new int[n];
//				int low[] = new int[n];
//				int hash[] = new int[n];
//				times = 0;
//				dfs(a[0]-1,g,vis,low,lvl,hash);
//				int cycles = 0; int cycle_nodes = 0;
//				DSU dsu = new DSU(n);
//				for(int i=0;i<n;i++) {
//					if(hash[low[i]]<i) {
//						dsu.union(hash[low[i]], i);
//					}else {
//						dsu.union(i,hash[low[i]]);
//					}
//				}
//				HashMap<Integer,Integer> s = new HashMap<Integer,Integer>();
//				for(int i=0;i<n;i++) {
//					int tmp = dsu.find(i);
//					s.put(tmp, s.getOrDefault(tmp, 0)+1);
//					//low[i] = s.get(dsu.find(i));
//				}
//				for(int i:s.keySet()) {
//					if(s.get(i)>1) {
//						cycles++;
//						cycle_nodes+=s.get(i);
//					}
//				}
//				if(k==3) {
//					//Dumper.print("here");
//				}
//				if(n-cycle_nodes+cycles>=k) {
//					System.out.println("YES");
//					//out.println("YES");
//					int temp [] = new int[n];
//					for(int i=0;i<n;i++) temp[i] = low[a[i]-1];
//					for(int i=1;i<n;i++) {
//						if(temp[i]>temp[i-1]+1) temp[i] = temp[i-1]+1;				
//						if(temp[i]>=k) temp[i] = temp[i-1];								
//					}
//					for(int i=0;i<n;i++) {
//						low[a[i]-1] = temp[i]; 
//					}
//					for(int i=0;i<n;i++) {
//						System.out.print((char)('a'+low[i]));
//						//out.print((char)('a'+low[i]));
//					}
//					System.out.println();
//					//out.println();
//				}
//				else {
//					System.out.println("NO");
//					//out.println("NO");	
//				}
//			//}
			int c = in.nextInt();
			while(c-->0) {
				int n = in.nextInt();
				int num[] = new int[n];
				int dlike[] = new int[n];
				int max = 0;
				for(int i=0;i<n;i++) {
					int t = in.nextInt()-1;
					int l = in.nextInt();
					num[t]++;
					if(l==1) dlike[t]++;
				}
				ArrayList<Integer>[] arr = new ArrayList[n+1];
				for(int i=0;i<=n;i++) arr[i] = new ArrayList<Integer>();
				for(int i=0;i<n;i++) {
					if(num[i]>0) arr[num[i]].add(dlike[i]);
					if(num[i]>max) max = num[i];
				}
				int cnt = 0;
				int ddlike = 0;
				PriorityQueue<Integer> pq = new PriorityQueue<Integer>(Collections.reverseOrder());
				for(int i=max;i>0;i--) {					
					pq.addAll(arr[i]);
					if(pq.isEmpty()) continue;
					cnt+=i;
					ddlike+=Math.min(i, pq.poll());
				}
				out.println(cnt+" "+ddlike);
			}
		}
		
		class pair implements Comparable<pair>{
			int num, like, dlike;
			public pair(int b, int c, int d) {
				num=b;like=c;dlike=d;
			}
			public int compareTo(pair x) {
				return x.dlike-this.dlike;
			}
		}		
		
	    public int maxLength(List<String> arr) {
	    	int n = arr.size();
	    	int w[] = new int[n];
	        int[][] a = new int[n][26];
	        for(int i=0;i<n;i++) {
	        	String tmp = arr.get(i);
	        	w[i] = tmp.length();
	        	for(int j=0;j<tmp.length();j++) {
	        		a[i][tmp.charAt(j)-'a']++;
	        		if(a[i][tmp.charAt(j)-'a']>1) w[i]=0;
	        	}
	        }
	        boolean g[][] = new boolean[n][n];	       
	        for(int i=0;i<n;i++) {
	        	for(int j=i+1;j<n;j++) {
	        		boolean flag = false;
	        		for(int k=0;k<26;k++) {
	        			if(a[i][k]!=0&&a[j][k]!=0) flag = true; 
	        		}
	        		if(!flag) g[i][j] = g[j][i] = true;
	        	}
	        }
	        int max = 0;
	        for(int i=0;i<(1<<n);i++) {
	        	boolean flag = true;
	        	for(int j=0;j<n;j++) {if((i&(1<<j))==0) continue;
	        		if((i&(1<<j))==0||!flag) continue;
	        		for(int k=j+1;k<n;k++) {
	        			if((i&(1<<k))==0||!flag) continue;
	        			if(!g[j][k]) flag = false;
	        		}
	        	}
	        	if(!flag) continue;
	        	//Dumper.print(i);
	        	int s = 0;
	        	for(int j=0;j<n;j++) if((i&(1<<j))==(1<<j)) s+=w[j];
	        	if(s>max) max = s;
	        }
	        return max;
	    }

		
		int dfs(int cur, ArrayList<Integer>[] g, boolean vis[], int low[], int[] lvl, int hash[]) {
			lvl[cur] = low[cur] = times;
			hash[times] = cur;
			times++;
			int reach = low[cur];
			vis[cur] = true;
			for(int to:g[cur]) {
				if(vis[to]) {
					reach = Math.min(reach, low[to]);
				}else {
					int tmp = dfs(to,g,vis,low,lvl,hash);
					reach = Math.min(reach, tmp);
				}
			}
			if(reach<low[cur]) low[cur] = reach;
			return low[cur];
		}
		class edge implements Comparable<edge>{
			int f,t,l,s;
			public edge(int a, int b, int c) {
				if(a<b){
					f=a;t=b;
				}else {
					f=b;t=a;
				}
				l=c;
			}
			@Override
			public int compareTo(edge t) {
				return this.l-t.l;
			}			
		}


			    	
		List<List<Integer>> convert(int arr[][]){
			int n = arr.length;
			List<List<Integer>> ret = new ArrayList<>();
			for(int i=0;i<n;i++) {
				ArrayList<Integer> tmp = new ArrayList<Integer>();
				for(int j=0;j<arr[i].length;j++) tmp.add(arr[i][j]);
				ret.add(tmp);
			}
			return ret;
		}
		
	    public int maximumSum(int[] arr) {
	        int n = arr.length;
	        int dp[][] = new int[n][2];
	        dp[0][0] = arr[0];
	        int ret = arr[0];
	        for(int i=1;i<n;i++) {
	        	dp[i][0] = dp[i-1][0]>=0?(dp[i-1][0]+arr[i]):arr[i];
	        	int t1 = dp[i-1][0];
	        	int t2 = (dp[i-1][1]<0?0:dp[i-1][1])+arr[i];
	        	dp[i][1] = Math.max(t1,t2);
	        	ret = Math.max(ret,Math.max(dp[i][0], dp[i][1]));
	        } 
	        return ret;
	    }		
	    public List<Integer> findNumOfValidWords(String[] words, String[] puzzles) {
	        List<Integer> ret = new ArrayList<Integer>();
	        HashMap<Integer,Integer>[] mp = new HashMap[26];
	        for(int i=0;i<26;i++) mp[i] = new HashMap<Integer,Integer>();
	        //String p = "abcdz";
	        //Dumper.print(enc(p));
	        for(int i=0;i<words.length;i++) {
	        	int v = enc(words[i]);
	        	for(int j=0;j<words[i].length();j++) {
	        		mp[words[i].charAt(j)-'a'].put(v, 1);
	        	}
	        }
	        for(int i=0;i<puzzles.length;i++) {
	        	int n = puzzles[i].length();
	        	int t = 0;
	        	for(int j=1;j<1<<(n-1);j++) {
	        		int v = 0;
	        		for(int k=0;k<6;k++) {
	        			if((j&(1<<k))!=0) {
	        				v|=(1<<(puzzles[i].charAt(k)-'a'));
	        			}
	        		}
	        		v|=(1<<(puzzles[i].charAt(0)-'a'));   		
	        		//t+=search(v,mp[puzzles[i].charAt(0)-'a']);
	        	}
	        	ret.add(t);
	        }
	        return ret;
	    }	
	    int search(int x, HashMap<Integer,Integer> mp, HashSet<Integer> hs) {
	    	if(mp.containsKey(x)) return mp.get(x);
	    	if(x==0) return 0;
	    	int v = 0;
	    	for(int i=0;i<7;i++) {
	    		if((x&(1<<i))!=0) {
	    			int t = x;
	    			t^=(1<<i);
	    			if(!hs.contains(t)) {
	    				hs.add(t);
	    				v+=search(t,mp,hs);	    				
	    			}
	    		}
	    	}
	    	mp.put(x, v);	    	
	    	return v;
	    }
	    int enc(String x) {
	    	char[] arr = x.toCharArray();
	    	int v = 0;
	    	for(int i=0;i<arr.length;i++) {
	    		v|=1<<(arr[i]-'a');
	    	}
	    	return v;
	    }
		
		public class TreeNode {
			int val;
			TreeNode left;
			TreeNode right;
			TreeNode(int x) { val = x; }
		}
	
		public int GCD(int a, int b) {
		   if (b==0) return a;
		   return GCD(b,a%b);
		}
		public long GCD(long a, long b) {
			   if (b==0) return a;
			   return GCD(b,a%b);
			}		
	}
	
	
    static class ArrayUtils {
        static final long seed = System.nanoTime();
        static final Random rand = new Random(seed);

        public static void sort(int[] a) {
            shuffle(a);
            Arrays.sort(a);
        }

        public static void shuffle(int[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }

    }	
	static class BIT{
		int arr[];
		int n;
		public BIT(int a) {
			n=a;
			arr = new int[n];
		}
		int sum(int p) {
			int s=0;
			while(p>0) {
				s+=arr[p];
				p-=p&(-p);
			}
			return s;
		}
		void add(int p, int v) {
			while(p<n) {
				arr[p]+=v;
				p+=p&(-p);
			}
		}
	}
	static class DSU{
		int[] arr;
		int[] sz;
		public DSU(int n) {
			arr = new int[n];
			sz = new int[n];
			for(int i=0;i<n;i++) arr[i] = i;
			Arrays.fill(sz, 1);
		}
		public int find(int a) {
			if(arr[a]!=a) arr[a] = find(arr[a]);
			return arr[a];
		}
		public void union(int a, int b) {
			int x = find(a);
			int y = find(b);
			if(x==y) return;
			arr[y] = x;
			sz[x] += sz[y];
		}
		public int size(int x) {
			return sz[find(x)];
		}
	}	
	static class MinHeap<Key> implements Iterable<Key> {
		private int maxN;
		private int n;
		private int[] pq;
		private int[] qp;
		private Key[] keys;
		private Comparator<Key> comparator;
		
		public MinHeap(int capacity){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
		}
		
		public MinHeap(int capacity, Comparator<Key> c){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
			comparator = c;
		}			
		public boolean isEmpty()	{ return n==0; 	}
		public int size()			{ return n;		}
		public boolean contains(int i) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        return qp[i] != -1;
		}	
		public int peekIdx() {
	        if (n == 0) throw new NoSuchElementException("Priority queue underflow");
	        return pq[1];		
		}	
		public Key peek(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			return keys[pq[1]];
		}
		public int poll(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			int min = pq[1];
			exch(1,n--);
			down(1);
			assert min==pq[n+1];
			qp[min] = -1;
			keys[min] = null;		
			pq[n+1] = -1;
			return min;
		}
	    public void update(int i, Key key) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (!contains(i)) {
	        	this.add(i, key);
	        }else {
	        	keys[i] = key;
	        	up(qp[i]);
	        	down(qp[i]);
	        }
	    }	
		private void add(int i, Key x){
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (contains(i)) throw new IllegalArgumentException("index is already in the priority queue");
	        n++;
	        qp[i] = n;
	        pq[n] = i;
	        keys[i] = x;
	        up(n);
		}
		private void up(int k){
			while(k>1&&less(k,k/2)){
				exch(k,k/2);
				k/=2;
			}
		}
		private void down(int k){
			while(2*k<=n){
				int j=2*k;
				if(j<n&&less(j+1,j)) j++;
				if(less(k,j)) break;
				exch(k,j);
				k=j;
			}
		}
		
		public boolean less(int i, int j){
	        if (comparator == null) {
	            return ((Comparable<Key>) keys[pq[i]]).compareTo(keys[pq[j]]) < 0;
	        }
	        else {
	            return comparator.compare(keys[pq[i]], keys[pq[j]]) < 0;
	        }
		}

		public void exch(int i, int j){
	        int swap = pq[i];
	        pq[i] = pq[j];
	        pq[j] = swap;
	        qp[pq[i]] = i;
	        qp[pq[j]] = j;
		}

		@Override
		public Iterator<Key> iterator() {
			// TODO Auto-generated method stub
			return null;
		}
	}  	

    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int zcurChar;
        private int znumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (znumChars == -1)
                throw new InputMismatchException();
            if (zcurChar >= znumChars)
            {
            	zcurChar = 0;
                try
                {
                    znumChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (znumChars <= 0)
                    return -1;
            }
            return buf[zcurChar++];
        }

        public int nextInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return nextString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }        
    }    

	static class Dumper {
		static void print_int_arr(int[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_char_arr(char[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_double_arr(double[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(int[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(boolean[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print(Object o) {
			System.out.println(o.toString());
		}

		static void getc() {
			System.out.println("here");
		}
	}
}