You are given a sequence $A_1, A_2, \ldots, A_N$. For each valid $i$, the star value of the element $A_i$ is the number of valid indices $j < i$ such that $A_j$ is divisible by $A_i$.
Chef is a curious person, so he wants to know the maximum star value in the given sequence. Help him find it.

-----Input-----
- The first line of the input contains a single integer $T$ which denotes the number of test cases.
- The first line of each test case contains a single integer $N$ .
- The second line of each test case contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum star value.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$ 
- Sum of $N$ over all test cases does not exceed $100,000$.

-----Subtasks-----
Subtask #1 (20 points): sum  of $N$ over all test cases does not exceed $5,000$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
7
8 1 28 4 2 6 7

-----Example Output-----
3

-----Explanation-----
$A_5 = 2$ divides $4$, $28$ and $8$, so its star value is $3$. There is no element with a higher star value.

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
T = int(input())
for _ in range(T):
	n = int(input())
	arr = list(map(int, input().split()))
	a = [0 for _ in range(max(arr) + 1)]
	star_val = []
	for i in range(len(arr)):
		j = 1
		val = 0
		while j * arr[i] <= len(a):
			val += a[j * arr[i] - 1]
			j += 1
		star_val.append(val)
		a[arr[i] - 1] += 1
	print(max(star_val))


T = int(input())
for _ in range(T):
	n = int(input())
	arr = list(map(int, input().split()))
	values = []
	if len(arr) == 1:
		print(0)
	else:
		for i in range(1, len(arr)):
			star = 0
			for j in range(i):
				if arr[j] % arr[i] == 0:
					star += 1
			values.append(star)
		print(max(values))


for t in range(int(input())):
	n = int(input())
	l = list(map(int, input().split()))
	l1 = []
	for i in range(len(l)):
		c = 0
		for j in range(i):
			if l[j] % l[i] == 0:
				c += 1
		l1.append(c)
	print(max(l1))


for _ in range(int(input())):
	n = int(input())
	lst = list(map(int, input().split()))
	val = 0
	for i in range(n - 1, -1, -1):
		temp = 0
		for j in range(i - 1, -1, -1):
			if lst[j] % lst[i] == 0:
				temp = temp + 1
		if temp >= val:
			val = temp
		if val == i:
			break
	print(val)


import sys
from math import sqrt
input = sys.stdin.readline
t = int(input())
for _ in range(t):
	n = int(input())
	a = list(map(int, input().strip().split()))
	max_star = [0] * (10 ** 6 + 5)
	ans = 0
	for i in range(n):
		x = a[i]
		if i > 0:
			ans = max(ans, max_star[x])
		for j in range(1, int(sqrt(x)) + 1):
			if x % j == 0:
				tempnum = int(x / j)
				if j != tempnum:
					max_star[j] += 1
					max_star[tempnum] += 1
				else:
					max_star[j] += 1
	print(ans)


for u in range(int(input())):
	n = int(input())
	x = [int(w) for w in input().split()]
	ans = 0
	for i in range(1, n):
		c = 0
		for j in range(i):
			if x[j] % x[i] == 0:
				c += 1
		ans = max(ans, c)
	print(ans)


import math
from functools import reduce

def printDivisors(n):
	return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0))))
for _ in range(int(input())):
	n = int(input())
	if n > 10 ** 4:
		List = [int(y) for y in input().split()]
		Dict = dict()
		Answ = 0
		for i in range(n):
			Divisor_List = printDivisors(List[i])
			if List[i] in Dict:
				if Dict[List[i]] > Answ:
					Answ = Dict[List[i]]
			for i in Divisor_List:
				if i in Dict:
					Dict[i] += 1
				else:
					Dict[i] = 1
		print(Answ)
	else:
		a = list(map(int, input().split()))
		h = [0] * 1000001
		m = 0
		for j in range(n - 1, 1, -1):
			x = j - 1
			c = 0
			if h[a[j]] == 0:
				while x >= 0:
					if a[x] % a[j] == 0:
						h[a[x]] = 1
						c = c + 1
					x = x - 1
				m = max(m, c)
				h[a[j]] = 1
		print(m)


import math
from functools import reduce

def printDivisors(n):
	return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0))))
for _ in range(int(input())):
	N = int(input())
	List = [int(y) for y in input().split()]
	Dict = dict()
	Answ = 0
	for i in range(N):
		Divisor_List = printDivisors(List[i])
		if List[i] in Dict:
			if Dict[List[i]] > Answ:
				Answ = Dict[List[i]]
		for i in Divisor_List:
			if i in Dict:
				Dict[i] += 1
			else:
				Dict[i] = 1
	print(Answ)


for _ in range(int(input())):
	N = int(input())
	L = list(map(int, input().split()))
	L2 = [0] * N
	res = 0
	n = N - 1
	while n != 0:
		if L2[n] == 1:
			n = n - 1
			continue
		req = 0
		a = L[n]
		for i in range(n - 1, -1, -1):
			if L[i] % L[n] == 0:
				L2[i] = 1
				req = req + 1
		res = max(req, res)
		n = n - 1
	print(res)


t = int(input())
for z in range(t):
	n = int(input())
	a = list(map(int, input().split()))
	h = [0] * 1000001
	m = 0
	for j in range(n - 1, 1, -1):
		x = j - 1
		c = 0
		if h[a[j]] == 0:
			while x >= 0:
				if a[x] % a[j] == 0:
					h[a[x]] = 1
					c = c + 1
				x = x - 1
			m = max(m, c)
			h[a[j]] = 1
	print(m)


from sys import stdin
from numpy import arange, array
for _ in arange(int(stdin.readline())):
	N = int(stdin.readline())
	a = array(list(map(int, stdin.readline().split())))
	h = [0] * N
	maxx = 0
	for j in range(N - 1, 1, -1):
		k = 0
		if h[j] == 0:
			for i in range(j + 1):
				if a[i] % a[j] == 0:
					k += 1
					h[i] = 1
		maxx = max(k - 1, maxx)
	print(maxx)


from numpy import arange, array
from sys import stdin
for _ in arange(int(stdin.readline())):
	N = int(stdin.readline())
	a = array(list(map(int, stdin.readline().split())))
	b = array(a[::-1])
	maxx = 0
	h = array([0] * N)
	for (index, items) in enumerate(b):
		k = 0
		if h[N - index - 1] == 0:
			for i in range(N - index):
				if a[i] % items == 0:
					k += 1
					h[i] = 1
		maxx = max(k - 1, maxx)
	print(maxx)


import numpy as np
for _ in range(int(input())):
	N = int(input())
	a = np.array(list(map(int, input().split())))
	b = np.array(a[::-1])
	maxx = 0
	h = np.array([0] * N)
	for (index, items) in enumerate(b):
		k = 0
		if h[N - index - 1] == 0:
			for i in range(N - index):
				if a[i] % items == 0:
					k += 1
					h[i] = 1
		maxx = max(k - 1, maxx)
	print(maxx)


for _ in range(int(input())):
	N = int(input())
	a = list(map(int, input().split()))
	b = a[::-1]
	maxx = 0
	h = [0] * N
	for (index, items) in enumerate(b):
		k = 0
		if h[N - index - 1] == 0:
			for i in range(N - index):
				if a[i] % items == 0:
					k += 1
					h[i] = 1
		maxx = max(k - 1, maxx)
	print(maxx)


for _ in range(int(input())):
	N = int(input())
	a = list(map(int, input().split()))
	b = a[::-1]
	maxx = 0
	dic = {}
	for (index, items) in enumerate(b):
		k = 0
		try:
			if dic[items] == 0:
				pass
		except Exception as e:
			for i in range(N - index):
				if a[i] % items == 0:
					k += 1
					dic[a[i]] = 0
		maxx = max(k - 1, maxx)
	print(maxx)