Codeforces Round #643 (Div. 2) : Young Explorers :solution in python

B. Young Explorers

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Young wilderness explorers set off to their first expedition led by senior explorer Russell. Explorers went into a forest, set up a camp and decided to split into groups to explore as much interesting locations as possible. Russell was trying to form groups, but ran into some difficulties...

Most of the young explorers are inexperienced, and sending them alone would be a mistake. Even Russell himself became senior explorer not long ago. Each of young explorers has a positive integer parameter ei

 — his inexperience. Russell decided that an explorer with inexperience e can only join the group of e

or more people.

Now Russell needs to figure out how many groups he can organize. It's not necessary to include every explorer in one of the groups: some can stay in the camp. Russell is worried about this expedition, so he asked you to help him.

Input

The first line contains the number of independent test cases T

(1≤T≤2⋅105). Next 2T

lines contain description of test cases.

The first line of description of each test case contains the number of young explorers N

(1≤N≤2⋅105

).

The second line contains N

integers e1,e2,…,eN (1≤ei≤N), where ei is the inexperience of the i

-th explorer.

It's guaranteed that sum of all N

doesn't exceed 3⋅105

.

Output

Print T

numbers, each number on a separate line.

In i

-th line print the maximum number of groups Russell can form in i

-th test case.

Example

Input

Copy

2
3
1 1 1
5
2 3 1 2 2

Output

Copy

3
2

Note

In the first example we can organize three groups. There will be only one explorer in each group. It's correct because inexperience of each explorer equals to 1

, so it's not less than the size of his group.

In the second example we can organize two groups. Explorers with inexperience 1

, 2 and 3 will form the first group, and the other two explorers with inexperience equal to 2

will form the second group.

This solution is not unique. For example, we can form the first group using the three explorers with inexperience equal to 2

, and the second group using only one explorer with inexperience equal to 1. In this case the young explorer with inexperience equal to 3 will not be included in any group.

Solution in Python :

t = int(input())
ar = []
for i in range(t) :
    n = int(input())
    e = [int(i) for i in input().split()]
    e.sort()
    mul = 0 ; count = 0 ; count1 = 1 ; sumif = 0 ;sumelse = 0
    for i in e:
        if i == 1 :
            count += 1
        else :
            if mul <count1**2 :
                if count1 == 1:
                    mul = 1
                mul *= i
                count1 += 1
                sumif += 1
            else :
                count1 = 1
                mul = 0
                count += 1
                sumelse += 1
    if sumif <sumelse :
        count -= 1
    elif sumif >sumelse :
        count += 1
    ar.append(count)
for i in ar :
    print(i)