Problem: This problem is actually a subproblem of problem G from the same contest.

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.

Your task is to find out the maximum possible size of the single gift you can prepare using the candies you have.

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. Each query is represented by two lines.

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

The second line of each query contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n), where a_i is the type of the i-th candy in the box.

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

Output

For each query print one integer — the maximum possible size of the single gift you can compose using candies you got in this query with the restriction described in the problem statement.

Example

Input


3
8
1 4 8 4 5 6 3 8
16
2 1 3 3 4 3 4 4 1 3 2 2 2 4 1 1
9
2 2 4 4 4 7 7 7 7


Output


3
10
9

Note

In the first query, you can prepare a gift with two candies of type 8 and one candy of type 5, totalling to 3 candies.

Note that this is not the only possible solution — taking two candies of type 4 and one candy of type 6 is also valid.

Solution (in JAVA):

Solution:
//Created by Aminul on 6/26/2019.

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class G {
    static BinaryIndexTree bit;

    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int test = in.nextInt();
        for (int t = 1; t <= test; t++) {
            int n = in.nextInt();
            int f[] = new int[n + 1], p[] = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                int x = in.nextInt();
                f[x]++;
                p[x] += in.nextInt();
            }
            long ans[] = solve(n, f, p);
            pw.println(ans[0] + " " + ans[1]);
        }

        pw.close();
    }

    static long[] solve(int n, int f[], int p[]) {
        long maxPossible = 0, maxOne = 0;
        Pair pairs[] = new Pair[n];
        for (int i = 1; i <= n; i++) {
            pairs[i - 1] = new Pair(f[i], p[i]);
        }
        Arrays.sort(pairs, (i, j) -> Integer.compare(j.s, i.s));
        bit = new BinaryIndexTree(n + 5);
        for (Pair pair : pairs) {
            int x = pair.f;
            int y = binarySearch(x);
            if (y <= 0) continue;
            maxPossible += y;
            maxOne += Math.min(y, pair.s);
            bit.add(y, 1);
        }
        return new long[]{maxPossible, maxOne};
    }
    
    static int binarySearch(int H) {
        int lo = 0, hi = H, mid;
        while (lo < hi) {
            mid = (lo + hi) / 2;
            if (bit.query(mid, H) >= (H - mid + 1)) hi = mid;
            else lo = mid + 1;
        }
        if (lo > 0 && bit.query(lo, H) >= H - lo + 1) lo--;
        return lo;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class Pair implements Comparable<Pair> {
        int f, s;

        Pair(int F, int S) {
            f = F;
            s = S;
        }

        public int compareTo(Pair p) {
            if (f == p.f) return s - p.s;
            return f - p.f;
        }

        public String toString() {
            return f + " " + s;
        }
    }

    static class BinaryIndexTree {
        public int bit[], n;

        public BinaryIndexTree(int N) {
            n = N;
            bit = new int[n];
        }

        public void add(int index, int value) {
            for (; index < n; index = index + (index & -index)) {
                bit[index] += value;
            }
        }

        public int sum(int index) {
            int sum = 0;
            for (; index > 0; index = index - (index & -index)) {
                sum += bit[index];
            }
            return sum;
        }

        public int query(int i, int j) {
            return sum(j) - sum(i - 1);
        }
    }
}