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 PYTHON3):

Solution:
from sys import stdin, stdout
M = lambda:list(map(int,stdin.readline().split()))

q = int(stdin.readline())
for qur in range(q):
    n = int(stdin.readline())
    C = [0] * (n + 1)
    F = [0] * (n + 1)
    for i in range(n):
        a, f = M()
        F[a] += f
        C[a] += 1
    C = [(C[i], F[i]) for i in range(1, n + 1)]
    C.sort(reverse = True)
    s = set()
    ans = 0
    nm = 0
    i = 0
    for mx in range(n, 0, -1):
        while i < len(C) and C[i][0] == mx:
            s.add((C[i][1], i))
            i += 1
        if len(s):
            e = max(s)
            ans += mx
            nm += min(e[0], mx)
            s.remove(e)
    stdout.write(str(ans)+" "+str(nm)+"\n")