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Raja only participates in contests and does not upsolve, but he claims that he has been upsolving. Chef wants to test if he is really improving, so he asks Raja to solve the following problem.

The median of a sequence of numbers is computed in the following way:
sort the sequence in non-decreasing order
if the number of elements of this sequence is odd, the median is its middle element
if the number of elements is even, the median is the average (arithmetic mean) of its two middle elements

For example, the median of $[1, 3, 2]$ is $2$ and the median of $[2, 3, 3, 2]$ is $(2+3)/2 = 5/2$.

You are given a sequence $A_{1}, A_{2}, \dots, A_{N}$. Let's call a subsequence $A_{i_{1}}, A_{i_{2}}, \dots, A_{i_{k}}$ (for any $k > 0$, $1 ≤ i_{1} < i_{2} < \ldots < i_{k} ≤ N$) *good* if the median of this subsequence is an element of this subsequence. Find the number of good subsequences. Since this number may be large, compute it modulo $1000000007$ ($10^{9}+7$).

------  Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \dots, A_{N}$.

------  Output ------
For each test case, print a single line containing one integer — the number of good subsequences modulo $10^{9}+7$.

------  Constraints ------
$1 ≤ T ≤ 30$
$1 ≤ N ≤ 1,000$
$1 ≤ A_{i} ≤ 2N$ for each valid $i$

------  Subtasks ------
Subtask #1 (5 points): $A$ is a permutation of integers $1$ through $N$

Subtask #2 (25 points): $1 ≤ N ≤ 100$

Subtask #3 (70 points): original constraints

----- Sample Input 1 ------ 
1

3

2 3 2
----- Sample Output 1 ------ 
5
----- explanation 1 ------ 
Example case 1: The good subsequences are $[2]$, $[3]$, $[2]$, $[2,2]$, $[2,3,2]$.

Difficulty: HARD
Tags: Combinatorics

Mathematics

Starter code:

Solutions:
def main():
	(mod, m) = (int(1000000000.0 + 7), 1005)
	(Fact, iFact) = ([1] * m, [1] * m)
	for i in range(2, m):
		Fact[i] = Fact[i - 1] * i % mod
		iFact[m - 1] = pow(Fact[m - 1], mod - 2, mod)
	for i in range(m - 2, 0, -1):
		iFact[i] = iFact[i + 1] * (i + 1) % mod
	t = int(input())
	for _ in range(t):
		n = int(input())
		arr = sorted(map(int, input().split()))
		ans = 0
		for i in range(n):
			for j in range(i, n):
				if i == j or arr[i] == arr[j]:
					(l, r) = (i, n - j - 1)
					ans += Fact[l + r] * iFact[l] * iFact[r] % mod
				else:
					break
		print(ans % mod)
main()


def main():
	(N, M) = (1005, int(1000000000.0 + 7))
	(F, IF) = ([1] * N, [1] * N)
	for i in range(1, N):
		F[i] = F[i - 1] * i % M
	IF[N - 1] = pow(F[N - 1], M - 2, M)
	for i in range(N - 2, 0, -1):
		IF[i] = IF[i + 1] * (i + 1) % M
	for _ in range(int(input())):
		n = int(input())
		arr = list(map(int, input().split()))
		arr.sort()
		res = 0
		for i in range(n):
			for j in range(i, n):
				if i == j:
					(l, r) = (i, n - i - 1)
					res += F[l + r] * IF[l] * IF[r]
				elif arr[i] == arr[j]:
					(l, r) = (i, n - j - 1)
					res += F[l + r] * IF[l] * IF[r]
				else:
					break
		print(res % M)
main()


def main():
	(N, M) = (2222, 1000000007)
	(F, IF) = ([1] * N, [1] * N)
	for i in range(1, N):
		F[i] = F[i - 1] * i % M
	IF[N - 1] = pow(F[N - 1], M - 2, M)
	for i in range(N - 2, 0, -1):
		IF[i] = IF[i + 1] * (i + 1) % M
	for _ in range(int(input())):
		n = int(input())
		a = list(map(int, input().split()))
		a.sort()
		res = 0
		for i in range(n):
			for j in range(i, n):
				if i == j:
					(l, r) = (i, n - i - 1)
					res += F[l + r] * IF[l] * IF[r]
				elif a[i] == a[j]:
					(l, r) = (i, n - j - 1)
					res += F[l + r] * IF[l] * IF[r]
				else:
					break
		print(res % M)
main()


def modinv(v, m):
	v %= m
	pv = m
	pc = 0
	c = 1
	while v > 0:
		(q, a) = divmod(pv, v)
		(pc, c) = (c, pc - q * c)
		(pv, v) = (v, a)
	return pc % m
mdl = 1000000007
lim = 1001
fac = 1
facm = [1]
for n in range(1, lim):
	fac = n * fac % mdl
	facm.append(fac)
ifac = modinv(fac, mdl)
invfm = [1] * lim
for n in reversed(range(1, lim)):
	invfm[n] = ifac
	ifac = n * ifac % mdl

def bc(n, k):
	if k == 0 or k == n:
		return 1
	return facm[n] * invfm[k] * invfm[n - k] % mdl
for ti in range(int(input())):
	n = int(input())
	ays = list(map(int, input().split()))
	oddseq = pow(2, n - 1, mdl)
	ays.sort()
	evnseq = 0
	ax = 0
	while ax < n - 1:
		a = ays[ax]
		bx = ax + 1
		if ays[bx] == a:
			while bx < n and ays[bx] == a:
				bx += 1
			r = bx - ax - 1
			if r == 1:
				evnseq += bc(n - 2, ax)
			else:
				evnseq += bc(n - r - 1, ax)
				evnseq += sum((bc(n, ci) for ci in range(ax + 2, ax + r, 2)))
				if r % 2 == 0:
					evnseq += bc(n - 1, ax + r - 1)
			evnseq %= mdl
		ax = bx
	print((oddseq + evnseq) % mdl)


M = 10 ** 9 + 7
f = [1] + [None] * 1000
for i in range(1, 1001):
	f[i] = f[i - 1] * i % M
rf = [0] * 1001 + [pow(f[1000], M - 2, M)]
for i in range(1000, 0, -1):
	rf[i] = rf[i + 1] * i % M
C = lambda i, j: f[i] * rf[j + 1] * rf[i - j + 1]
t = int(input())
for _ in range(t):
	n = int(input())
	a = sorted(map(int, input().split()))
	r = pow(2, n, M) - 1
	x0 = 0
	for (i, x) in enumerate(a):
		if x > x0:
			(i0, x0) = (i - 1, x)
		r -= C(i0 + n - i, i0)
	print(r % M)


from sys import stdin
dp = [[0 for x in range(1001)] for y in range(1001)]
for i in range(1001):
	for j in range(i + 1):
		if i == j or j == 0:
			dp[i][j] = 1
		else:
			dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]
T = int(stdin.readline())
for k in range(T):
	N = int(stdin.readline())
	arr = list(map(int, stdin.readline().split()))
	count = 0
	arr.sort()
	for i in range(N):
		for j in range(i + 1, N):
			if arr[i] == arr[j]:
				count += dp[i + N - 1 - j][i]
			else:
				break
	print(((1 << N - 1) % 1000000007 + count) % 1000000007)


mdl = 1000000007
lim = 1000
coeff = [[1] * (n + 1) for n in range(lim)]
tc = coeff[0]
for n in range(1, lim):
	lc = tc
	tc = coeff[n]
	for k in range(1, n // 2 + 1):
		tc[n - k] = tc[k] = (lc[k - 1] + lc[k]) % mdl

def bc(n, k):
	if k < 0 or k > n:
		return 0
	return coeff[n][k]
for ti in range(int(input())):
	n = int(input())
	ays = list(map(int, input().split()))
	oddseq = pow(2, n - 1, mdl)
	ays.sort()
	evnseq = 0
	ax = 0
	while ax < n - 1:
		a = ays[ax]
		bx = ax + 1
		if ays[bx] == a:
			while bx < n and ays[bx] == a:
				bx += 1
			r = bx - ax - 1
			out = n - 2
			for g in range(r):
				evnseq += sum(coeff[out][ax:ax + r - g])
				out -= 1
			evnseq %= mdl
		ax = bx
	print((oddseq + evnseq) % mdl)


MOD = 10 ** 9 + 7
table = [[1 for i in range(1001)] for j in range(1001)]
for i in range(1, 1001):
	for j in range(1, 1001):
		table[i][j] = (table[i][j - 1] + table[i - 1][j]) % MOD
t = int(input())
for _ in range(t):
	n = int(input())
	arr = [int(x) for x in input().strip().split()]
	sarr = set(arr)
	if len(sarr) == n:
		print(2 ** (n - 1) % MOD)
	else:
		arr = sorted(arr, reverse=False)
		(ga, gb) = (0, 0)
		while gb < n:
			tmp = gb
			mark = tmp + 1
			while mark < n:
				if arr[mark] == arr[tmp]:
					mark += 1
				else:
					break
			gb = mark
			for i in range(tmp, mark):
				for j in range(i, mark):
					(low, right) = (i, n - j - 1)
					val = 0
					val = table[low][right] % MOD
					ga = (ga + val) % MOD
		print(ga % MOD)


def power(x, y, p):
	res = 1
	x = x % p
	while y > 0:
		if y & 1 == 1:
			res = res * x % p
		y = y >> 1
		x = x * x % p
	return res
mod = 1000000007
fac = [0 for x in range(2001)]
fac[0] = 1
for i in range(1, 2001):
	fac[i] = fac[i - 1] * i % mod

def modInverse(n, p):
	return power(n, p - 2, p)

def nCrModPFermat(n, r, p):
	if r == 0:
		return 1
	return fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p % p
for T in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	a.sort()
	a.append(3000)
	dup = [1]
	pos_f = [0]
	pos_l = [0]
	j = 1
	for i in range(n):
		if a[i] == a[i + 1]:
			if dup[j - 1] == 1:
				pos_f[j - 1] = i
			dup[j - 1] += 1
		elif dup[j - 1] > 1:
			pos_l[j - 1] = i
			dup.append(1)
			pos_f.append(0)
			pos_l.append(0)
			j += 1
	ans = 0
	for i in range(j - 1):
		mi = min(pos_f[i] - 0, n - pos_l[i] - 1)
		ma = max(pos_f[i] - 0, n - pos_l[i] - 1)
		s_even = 0
		s_odd = 0
		l_even = 0
		l_odd = 1
		for k in range(2, dup[i] + 1):
			if k % 2 == 0:
				if l_even == 0 and mi + l_even <= ma + mi:
					s_even = (s_even + nCrModPFermat(ma + mi, mi + l_even, mod)) % mod
				else:
					if mi + l_even <= ma + mi:
						s_even = (s_even + nCrModPFermat(ma + mi, mi + l_even, mod)) % mod
					if ma + l_even <= ma + mi:
						s_even = (s_even + nCrModPFermat(ma + mi, ma + l_even, mod)) % mod
				l_even += 2
				ans = (ans + nCrModPFermat(dup[i], k, mod) * s_even) % mod
			else:
				if mi + l_odd <= ma + mi:
					s_odd = (s_odd + nCrModPFermat(ma + mi, mi + l_odd, mod)) % mod
				if ma + l_odd <= ma + mi:
					s_odd = (s_odd + nCrModPFermat(ma + mi, ma + l_odd, mod)) % mod
				l_odd += 2
				ans = (ans + nCrModPFermat(dup[i], k, mod) * s_odd) % mod
	ans = (ans + power(2, n - 1, mod)) % mod
	print(ans)


def readInt():
	return int(input())

def readInts():
	return [int(x) for x in input().split()]

def cases():
	numCases = readInt()
	for _ in range(numCases):
		n = readInt()
		seq = readInts()
		yield (n, seq)
medianWays = [[[0, 0] for _ in range(1001)] for _ in range(1001)]
for n in range(1, 1001):
	for m in range(n - 1):
		medianWays[n][m][0] = (medianWays[n - 1][m][0] + medianWays[n - 1][m][1]) % 1000000007
		medianWays[n][m][1] = (medianWays[n - 1][n - m - 2][0] + medianWays[n - 1][m][1]) % 1000000007
	medianWays[n][n - 1][1] = 1

def calcWays(n, lastPos, groupSize):
	left = lastPos + 1 - groupSize
	result = 0
	for p1 in range(1, groupSize):
		for p2 in range(p1 + 1, groupSize + 1):
			result = (result + medianWays[n - (p2 - p1 - 1)][left + p1][0]) % 1000000007
	return result

def solve(n, seq):
	seq.sort()
	ways = pow(2, n - 1, 1000000007)
	for (p, e) in enumerate(seq):
		otherp = p + 1
		while otherp < n and seq[otherp] == e:
			pairDist = otherp - p
			ways = (ways + medianWays[n - pairDist][p][1]) % 1000000007
			otherp += 1
	return ways
for data in cases():
	print(solve(*data))


arr = [[0 for x in range(1001)] for y in range(1001)]
for i in range(1001):
	for j in range(i + 1):
		if i == j or j == 0:
			arr[i][j] = 1
		else:
			arr[i][j] = arr[i - 1][j - 1] + arr[i - 1][j]
modu = 1000000007
t = int(input())
while t > 0:
	n = int(input())
	a = []
	a = [int(i) for i in input().split()]
	a.sort()
	ans = 0
	p = 1
	while p <= n:
		ans = ans + arr[n][p]
		p = p + 2
	for i in range(n - 1):
		for j in range(i + 1, n):
			if a[i] == a[j]:
				ans = ans + arr[i + n - 1 - j][i]
	print(ans % modu)
	t = t - 1


from sys import stdin
a = []
for i in range(1001):
	a.append([])
	a[i].append(1)
	for j in range(1, i):
		a[i].append((a[i - 1][j - 1] + a[i - 1][j]) % (10 ** 9 + 7))
	if i != 0:
		a[i].append(1)
a[0] = [1]
for _ in range(int(stdin.readline())):
	n = int(stdin.readline())
	b = [int(x) for x in stdin.readline().split()]
	c = 0
	if n % 2 != 0:
		ulim = n
	else:
		ulim = n - 1
	for i in range(ulim, -1, -2):
		c = (c + a[n][n - i]) % (10 ** 9 + 7)
	ulim = n - 2
	b = sorted(b)
	for i in range(n - 1):
		rec = 0
		for j in range(i + 1, n):
			if b[i] == b[j]:
				c = (c + a[ulim - rec][i]) % (10 ** 9 + 7)
				rec += 1
			else:
				break
	print(c)


a = []
for i in range(1001):
	a.append([])
	a[i].append(1)
	for j in range(1, i):
		a[i].append((a[i - 1][j - 1] + a[i - 1][j]) % (10 ** 9 + 7))
	if i != 0:
		a[i].append(1)
a[0] = [1]
for _ in range(int(input())):
	n = int(input())
	b = [int(x) for x in input().split()]
	c = 0
	if n % 2 == 0:
		ulim = n - 1
	else:
		ulim = n
	for i in range(ulim, -1, -2):
		c = (c + a[n][n - i]) % (10 ** 9 + 7)
	ulim = n - 2
	b = sorted(b)
	for i in range(n - 1):
		rec = 0
		for j in range(i + 1, n):
			if b[i] == b[j]:
				c = (c + a[ulim - rec][i]) % (10 ** 9 + 7)
				rec += 1
			else:
				break
	print(c)


M = 1000000007
C = None
SC = None

def genC(n, M):
	C = [[0 for j in range(n + 1)] for i in range(n + 1)]
	for i in range(n + 1):
		C[i][0] = 1
	for i in range(1, n + 1):
		for j in range(1, n + 1):
			C[i][j] = C[i - 1][j] + C[i - 1][j - 1]
	return C

def genSC(n, M):
	SC = [[0 for j in range(n + 1)] for i in range(n + 1)]
	for i in range(n + 1):
		SC[i][0] = C[i][0]
	for i in range(1, n + 1):
		for j in range(1, n + 1):
			SC[i][j] = (C[i][j] % M + SC[i][j - 1] % M) % M
	return SC

def series_sum(l1, l2, m):
	if l1 > l2:
		(l1, l2) = (l2, l1)
	s = 0
	for i in range(m - 1):
		if l1 == 0:
			s = (s % M + SC[l1 + l2 + m - 2 - i][l1 + m - 2 - i] % M) % M
		else:
			s = (s % M + (SC[l1 + l2 + m - 2 - i][l1 + m - 2 - i] % M - SC[l1 + l2 + m - 2 - i][l1 - 1] % M + M) % M) % M
	return s

def findSubs(arr, M):
	arr.sort()
	sum_e = 0
	sum_o = 0
	i = 0
	while i < len(arr) - 1:
		j = i + 1
		while j < len(arr) and arr[j] == arr[i]:
			j += 1
		sum_e = (sum_e % M + series_sum(i, len(arr) - j, j - i) % M) % M
		i = j
	sum_o = pow(2, len(arr) - 1, M)
	total = (sum_e + sum_o) % M
	return total
C = genC(1000, M)
SC = genSC(1000, M)
t = int(input())
for _ in range(t):
	int(input())
	arr = [int(i) for i in input().split()]
	print(findSubs(arr, M))


from collections import defaultdict
mod = 10 ** 9 + 7
l2 = [[0 for i in range(1001)] for j in range(1001)]
l1 = [[0 for i in range(1001)] for j in range(1001)]
l2[0][0] = 1
for i in range(1, 999):
	l2[i][0] = 1
	for j in range(1, i + 1):
		l2[i][j] = (l2[i - 1][j - 1] + l2[i - 1][j]) % mod
		l1[i][j] += (l2[i][j] + l1[i - 1][j]) % mod
for i in range(int(input())):
	n = int(input())
	l = list(map(int, input().split()))
	l = sorted(l)
	ans = pow(2, n - 1, mod)
	d = defaultdict(int)
	for i in l:
		d[i] += 1
	for i in d:
		ans += l2[d[i]][2]
	for i in range(len(l) - 1):
		if l[i] == l[i + 1]:
			extra = n - i - d[l[i]]
			d[l[i]] -= 1
			start = n - i - 2
			for j in range(1, start + 1):
				if i < j:
					break
				if extra == 0:
					sum1 = l1[start][j]
				else:
					sum1 = l1[start][j] - l1[extra - 1][j]
				save = l2[i][j] * sum1
				if save == 0:
					break
				ans += save
				ans %= mod
	print(ans)


import math
mod = 10 ** 9 + 7
facts = [0] * 1001
invfacts = [0] * 1001
facts[0] = 1
invfacts[0] = 1
for i in range(1, 1001):
	facts[i] = facts[i - 1] * i % mod
	invfacts[i] = pow(facts[i], mod - 2, mod)

def ncr(n, r, k):
	su = 0
	for i in range(k, r + 1):
		su += facts[n] * invfacts[i] * invfacts[n - i] % mod
	return su % mod
for t in range(int(input())):
	n = int(input())
	arr = list(map(int, input().split()))
	arr.sort()
	s = pow(2, n - 1, mod)
	(i, count) = (0, 1)
	while i < n - 1:
		if arr[i] == arr[i + 1]:
			count += 1
		elif count > 1:
			for it in range(2, count + 1):
				s += ncr(n - it, i + 1 - it, i - count + 1)
			s %= mod
			count = 1
		i += 1
	if count > 1:
		for it in range(2, count + 1):
			s += ncr(n - it, i + 1 - it, i - count + 1)
	print(s % mod)


ghat = 1000000007
sala = [[1 for x in range(1001)] for j in range(1001)]
for i in range(1, 1001):
	for j in range(1, 1001):
		sala[i][j] = (sala[i - 1][j] + sala[i][j - 1]) % ghat
for T in range(int(input())):
	n = int(input())
	ar = list(map(int, input().split()))
	ar.sort()
	baby = 0
	bara = 0
	while bara < n:
		gandu = bara
		chup = gandu + 1
		while chup < n and ar[chup] == ar[gandu]:
			chup += 1
		bara = chup
		dher = chup - 1
		for i in range(gandu, dher + 1):
			for j in range(i, dher + 1):
				badike = i
				dandike = n - j - 1
				chor = sala[badike][dandike]
				baby = (baby + chor) % ghat
	print(baby % ghat)


from bisect import bisect_left as bl
mod = 1000000007

def po(n):
	a = 1
	for i in range(n):
		a *= 2
		a %= mod
	return a
bigdaddyarray = [[0] * 1001 for i in range(1001)]
bigdaddyarray[0][0] = 1
for i in range(1, 1001):
	bigdaddyarray[i][1] = i
for i in range(1, 1001):
	bigdaddyarray[i][0] = 1
for i in range(2, 1001):
	bigdaddyarray[1][i] = 0
for i in range(2, 1001):
	for j in range(2, 1001):
		bigdaddyarray[i][j] = bigdaddyarray[i - 1][j] + bigdaddyarray[i - 1][j - 1]
for _ in range(int(input())):
	n = int(input())
	a = sorted(list(map(int, input().split())))
	d = {}
	for i in a:
		d[i] = d.get(i, 0) + 1
	ans = po(n - 1)
	for i in d.keys():
		if d[i] >= 2:
			m = bl(a, i)
			for j in range(m + 1, m + d[i]):
				r = 0
				for x in range(j + 1, m + d[i] + 1):
					ans += bigdaddyarray[n - r - 2][j - 1]
					r += 1
		ans %= mod
	print(ans)


(array, prefix) = ([], [])
for i in range(1001):
	array.append([1] * (i + 1))
	prefix.append([1] * (i + 1))
MOD = 10 ** 9 + 7
for i in range(2, 1001):
	for j in range(1, i):
		array[i][j] = array[i - 1][j - 1] + array[i - 1][j]
for i in range(1, 1001):
	for j in range(i):
		prefix[i][j] = prefix[i - 1][j] + array[i][j]
for _ in range(int(input())):
	n = int(input())
	ar = list(map(int, input().split()))
	ar.sort()
	(cur, minus) = (0, 0)
	for i in range(n):
		while cur < n and ar[i] == ar[cur]:
			cur += 1
		if cur >= n:
			break
		for j in range(min(i, n - cur - 1) + 1):
			minus += array[i][j] * prefix[n - cur - 1][j]
	print((2 ** n - 1 - minus) % MOD)


import numpy as np
M = int(1000000000.0 + 7)

def mod_pow(base, index):
	ret = 1
	while index > 0:
		if index & 1 == 1:
			ret = ret * base % M
		index = index >> 1
		base = base * base % M
	return ret

def inv_mod(n):
	return mod_pow(n, M - 2)
F = np.empty(1001, dtype=np.int64)
F[0] = 1
for i in range(1, 1001):
	F[i] = F[i - 1] * i % M
I = np.empty(1001, dtype=np.int64)
for i in range(1001):
	I[i] = inv_mod(i)
C = np.zeros((1001, 1001), dtype=np.int64)
Cum = np.zeros((1001, 1001), dtype=np.int64)
C[:, 0] = 1
A = np.arange(1001)
for x in range(1, 1001):
	C[:, x] = C[:, x - 1] * I[x] % M
	C[:, x] = C[:, x] * (A - x + 1) % M
Cum[0, :] = C[0, :]
for A in range(1, 1001):
	Cum[A, :] = (C[A, :] + Cum[A - 1, :]) % M

def cum_sum(A1, A2):
	if A1 == 0:
		return Cum[A2, :]
	else:
		return Cum[A2, :] - Cum[A1 - 1, :]
t = int(input())
for _ in range(t):
	n = int(input())
	A = list(map(int, input().split()))
	A.sort()
	next_A = [0 for _ in range(len(A))]
	next_A[n - 1] = n
	for i in range(n - 2, -1, -1):
		if A[i] == A[i + 1]:
			next_A[i] = next_A[i + 1]
		else:
			next_A[i] = i + 1
	ans = 0
	for i in range(len(A) - 1):
		if A[i] == A[i + 1]:
			prev = i
			A2 = n - i - 2
			A1 = n - next_A[i]
			ans = (ans + np.sum(C[prev, :] * cum_sum(A1, A2) % M) % M) % M
	ans = (ans + M) % M
	ans = (ans + mod_pow(2, len(A) - 1)) % M
	print(ans)


M = 10 ** 9 + 7
f = [1] + [None] * 999
rf = [1] + [None] * 999
for i in range(1, 1000):
	f[i] = f[i - 1] * i % M
	rf[i] = pow(f[i], M - 2, M)
choose = lambda i, j: f[i] * rf[j] * rf[i - j]
t = int(input())
for _ in range(t):
	n = int(input())
	a = sorted(map(int, input().split()))
	r = pow(2, n, M) - 1
	x0 = 0
	for (i, x) in enumerate(a):
		if x > x0:
			(i0, x0) = (i, x)
		i = n - i
		r -= sum((choose(i0, k + 1) * choose(i - 1, k) for k in range(min(i0, i))))
	print(r % M)


mod = 1000000007
import time

def modex(a, b):
	if b == 0:
		return 1
	if b % 2 == 0:
		y = modex(a, b / 2)
		return y % mod * (y % mod) % mod
	return a % mod * modex(a, b - 1) % mod

def modi(a):
	return modex(a, mod - 2) % mod

def main():
	nc = [[0 for x in range(2001)] for y in range(2001)]
	nc[0][0] = 1
	nc[1][0] = 1
	nc[1][1] = 1
	for i in range(2, 2001):
		nc[i][0] = 1
		for j in range(1, i + 1):
			nc[i][j] = (nc[i - 1][j] + nc[i - 1][j - 1]) % mod
	t = int(input())
	while True:
		n = int(input())
		a = [int(x) for x in input().split()]
		c = modex(2, n - 1)
		a.sort()
		for i in range(0, n - 1):
			for j in range(i + 1, n):
				if a[i] == a[j]:
					c = (c + nc[i + n - 1 - j][i]) % mod
		print(c)
		t = t - 1
		if t == 0:
			return
main()


ncr = [[1] * 1001 for i in range(1001)]
for j in range(1, 1001):
	temp = j
	for i in range(1, j):
		ncr[j][i] = temp
		temp = temp * (j - i)
		temp = temp // (i + 1)
ncr_sum = [[1] * 1001 for i in range(1001)]
for j in range(1, 1000):
	for i in range(j):
		ncr_sum[j][i] = ncr_sum[j - 1][i] + ncr[j][i]
for t in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	if n == 1:
		print('1')
		continue
	fre = [0] * 2001
	for i in a:
		fre[i] += 1
	count = 0
	for i in range(1, n + 1, 2):
		count = (count + ncr[n][i]) % 1000000007
	a.sort()
	i = 0
	while i < n - 1:
		if a[i] != a[i + 1]:
			i += 1
			continue
		j = i + fre[a[i]]
		c = fre[a[i]]
		n1 = i
		n2 = n - j
		while c > 1:
			c -= 1
			if n1 + n2 == 0:
				count = count + ncr_sum[n - 2][n2]
				n2 += 1
				continue
			if n1 < n2:
				count = count + (ncr_sum[n - 2][n1] - ncr_sum[n1 + n2 - 1][n1])
				n1 += 1
			else:
				count = count + (ncr_sum[n - 2][n2] - ncr_sum[n1 + n2 - 1][n2])
				n2 += 1
		i += fre[a[i]]
	print(count % 1000000007)


M = 10 ** 9 + 7
f = [1] + [None] * 1000
rf = [1] + [None] * 1000
for i in range(1, 1001):
	f[i] = f[i - 1] * i % M
	rf[i] = pow(f[i], M - 2, M)
c = lambda i, j: f[i] * rf[j] * rf[i - j]
t = int(input())
for _ in range(t):
	n = int(input())
	a = sorted(map(int, input().split()))
	r = pow(2, n, M) - 1
	i = 0
	while i < n:
		i1 = next((j for j in range(i + 1, n) if a[j] > a[i]), n)
		u = n - i1
		for j in range(i, i1):
			r -= sum((c(j, k) * c(u, k + 1) for k in range(min(j + 1, u))))
		i = i1
	print(r % M)


M = 10 ** 9 + 7
f = [1] + [None] * 1000
rf = [1] + [None] * 1000
for i in range(1, 1001):
	f[i] = f[i - 1] * i % M
	rf[i] = pow(f[i], M - 2, M)
c = lambda i, j: f[i] * rf[j] * rf[i - j]
t = int(input())
for _ in range(t):
	n = int(input())
	a = [0] * (2 * n)
	for i in map(int, input().split()):
		a[i - 1] += 1
	r = pow(2, n, M) - 1
	s = 0
	for x in a:
		(u, s) = (s, s + x)
		v = n - s
		for i in range(x):
			r -= sum((c(u, k) * c(v, k + 1) for k in range(min(u + 1, v))))
			u += 1
	print(r % M)


M = 10 ** 9 + 7
C = [1001 * [0] for x in range(1001)]
C[0][0] = 1
for i in range(1, 1001):
	C[i][0] = 1
	for j in range(1, i + 1):
		C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % M
t = int(input())
answer = 0
for _ in range(t):
	n = int(input())
	A = [int(x) for x in input().split()]
	A.sort()
	for i in range(len(A)):
		for j in range(i, len(A)):
			if A[i] == A[j]:
				answer = (answer + C[i + n - 1 - j][i]) % M
	print(answer)
	answer = 0


M = 1000000007
N = 1000
factorialNumInverse = [0 for i in range(N + 1)]
naturalNumInverse = [0 for i in range(N + 1)]
fact = [0 for i in range(N + 1)]

def InverseofNumber(p):
	naturalNumInverse[0] = naturalNumInverse[1] = 1
	for i in range(2, N + 1):
		naturalNumInverse[i] = naturalNumInverse[p % i] * (p - p // i) % p

def InverseofFactorial(p):
	factorialNumInverse[0] = factorialNumInverse[1] = 1
	for i in range(2, N + 1):
		factorialNumInverse[i] = naturalNumInverse[i] * factorialNumInverse[i - 1] % p

def factorial(p):
	fact[0] = 1
	for i in range(1, N + 1):
		fact[i] = fact[i - 1] * i % p
InverseofNumber(M)
InverseofFactorial(M)
factorial(M)

def nCr(n, r, p):
	return fact[n] * factorialNumInverse[r] % p * factorialNumInverse[n - r] % p
for _ in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	a.sort()
	sufInd = [0 for i in range(n)]
	sufInd[n - 1] = n - 1
	for i in range(n - 2, -1, -1):
		if a[i] == a[i + 1]:
			sufInd[i] = sufInd[i + 1]
		else:
			sufInd[i] = i
	finalAns = 0
	i = 0
	y = 0
	z = 0
	m = 0
	while i < n:
		m = sufInd[i] - i + 1
		y = i
		z = n - sufInd[i] - 1
		for j in range(2, m + 1):
			c1 = 0
			c2 = j - 2
			ans = 0
			for k in range(1, j):
				if c1 == 0 and y + c2 <= y + z:
					ans = (ans + nCr(y + z, y + c2, M)) % M
				elif c2 == 0 and z + c1 <= y + z:
					ans = (ans + nCr(y + z, z + c1, M)) % M
				c2 = c2 - 2
				if c2 < 0:
					if c1 == 0:
						c1 = -c2
					else:
						c1 += 2
					c2 = 0
			ans = ans * nCr(m, j, M) % M
			finalAns = (finalAns + ans) % M
		i = sufInd[i] + 1
	for i in range(1, n + 1, 2):
		finalAns = (finalAns + nCr(n, i, M)) % M
	print(finalAns)


import math
mod = 10 ** 9 + 7
facts = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 227020758, 178290591, 674358851, 789741546, 425606191, 660911389, 557316307, 146326063, 72847302, 602640637, 860734560, 657629300, 440732388, 459042011, 394134213, 35757887, 36978716, 109361473, 390205642, 486580460, 57155068, 943272305, 14530444, 523095984, 354551275, 472948359, 444985875, 799434881, 776829897, 626855450, 954784168, 10503098, 472639410, 741412713, 846397273, 627068824, 726372166, 318608048, 249010336, 948537388, 272481214, 713985458, 269199917, 75195247, 286129051, 595484846, 133605669, 16340084, 996745124, 798197261, 286427093, 331333826, 536698543, 422103593, 280940535, 103956247, 172980994, 108669496, 715534167, 518459667, 847555432, 719101534, 932614679, 878715114, 661063309, 562937745, 472081547, 766523501, 88403147, 249058005, 671814275, 432398708, 753889928, 834533360, 604401816, 187359437, 674989781, 749079870, 166267694, 296627743, 586379910, 119711155, 372559648, 765725963, 275417893, 990953332, 104379182, 437918130, 229730822, 432543683, 551999041, 407899865, 829485531, 925465677, 24826746, 681288554, 260451868, 649705284, 117286020, 136034149, 371858732, 391895154, 67942395, 881317771, 114178486, 473061257, 294289191, 314702675, 79023409, 640855835, 825267159, 333127002, 640874963, 750244778, 281086141, 979025803, 294327705, 262601384, 400781066, 903100348, 112345444, 54289391, 329067736, 753211788, 190014235, 221964248, 853030262, 424235847, 817254014, 50069176, 159892119, 24464975, 547421354, 923517131, 757017312, 38561392, 745647373, 847105173, 912880234, 757794602, 942573301, 156287339, 224537377, 27830567, 369398991, 365040172, 41386942, 621910678, 127618458, 674190056, 892978365, 448450838, 994387759, 68366839, 417262036, 100021558, 903643190, 619341229, 907349424, 64099836, 89271551, 533249769, 318708924, 92770232, 420330952, 818908938, 584698880, 245797665, 489377057, 66623751, 192146349, 354927971, 661674180, 71396619, 351167662, 19519994, 689278845, 962979640, 929109959, 389110882, 98399701, 89541861, 460662776, 289903466, 110982403, 974515647, 928612402, 722479105, 218299090, 96415872, 572421883, 774063320, 682979494, 693774784, 611379287, 166890807, 880178425, 837467962, 705738750, 616613957, 338771924, 497191232, 896114138, 560652457, 661582322, 224945188, 262995829, 859081981, 857116478, 279856786, 408062844, 406076419, 367193638, 985761614, 767884817, 77737051, 801784560, 410447512, 813374614, 702909132, 777826615, 11426636, 685259446, 721228129, 931065383, 593559607, 860745086, 578819198, 495425745, 893029457, 6156532, 502193801, 37480384, 220174401, 383076669, 3013247, 750298503, 574624441, 230733683, 144887710, 656590378, 773954850, 358485371, 772254339, 469363737, 95843299, 823414273, 87709482, 892174648, 749756145, 185864756, 68295241, 98238739, 131504392, 111672419, 928208089, 687974198, 753032165, 71715287, 506557931, 290314197, 546089425, 174590825, 187067364, 817659471, 309331349, 303445769, 964814732, 112937795, 848457973, 113604679, 263728612, 162653895, 519013648, 956915940, 591788795, 26960558, 818561771, 201473695, 830318534, 283328761, 298655153, 103269519, 567777414, 629890782, 707451727, 528064896, 419467694, 259775012, 452053078, 972081682, 512829263, 412924123, 354780756, 917691336, 648929514, 519218426, 957710940, 848100261, 607279584, 78508462, 651656900, 271922065, 927371945, 976904514, 655633282, 147015495, 44958071, 431540693, 956102180, 821001984, 4640954, 508310043, 709072863, 866824584, 318461564, 773853828, 371761455, 53040744, 609526889, 972452623, 799173814, 723225821, 3874155, 305590228, 289496343, 139259591, 348260611, 756867525, 848691744, 101266155, 835557082, 267191274, 448180160, 518514435, 443022120, 614718802, 151579195, 204297074, 912569551, 137049249, 515433810, 979001276, 524451820, 229298431, 88837724, 892742699, 387369393, 840349900, 206661672, 18186411, 619853562, 246548548, 236767938, 893832644, 930410696, 321544423, 971435684, 402636244, 780681725, 194281388, 661238608, 964476271, 643075362, 439409780, 96895678, 723461710, 915447882, 785640606, 114709392, 933696835, 539582134, 739120141, 300372431, 244129985, 722433522, 26638091, 388855420, 42468156, 647517040, 474194942, 832805846, 958306874, 489519451, 339220689, 9833277, 923477502, 390998217, 790283925, 694135631, 736657340, 609563281, 873127083, 489593220, 264439147, 891171227, 489029295, 502009550, 325923608, 280525558, 857054649, 820622208, 558213940, 216997416, 487921842, 951328535, 606653379, 794417402, 449723904, 783486165, 414645478, 809681447, 114612567, 824953206, 255016498, 147060381, 88903008, 228293174, 394357308, 362355866, 900088886, 638573794, 779598451, 904922263, 451026166, 549459329, 212643744, 563246709, 391796933, 174243175, 189725986, 238337196, 60051478, 782959006, 982673239, 237607992, 685987666, 694447544, 195840153, 519748540, 446086975, 523485236, 185780714, 716004996, 214280883, 140643728, 555470704, 516522055, 116665689, 899547947, 490696549, 683197147, 686671136, 988747143, 744912554, 619072836, 345158054, 224284246, 637879131, 78947725, 342273666, 237716550, 915360466, 711578771, 423071394, 228124918, 271834959, 480779410, 254894593, 859192972, 990202578, 258044399, 151532640, 644862529, 48049425, 448119239, 130306338, 850105179, 401639970, 606863861, 183881380, 837401090, 513536652, 714177614, 946271680, 243293343, 403377310, 688653593, 15447678, 754734307, 631353768, 202296846, 159906516, 912696536, 737140518, 467380526, 896686075, 309895051, 356369955, 461415686, 706245266, 10064183, 183054210, 455971702, 737368289, 956771035, 564163693, 365118309, 226637659, 304857172, 440299843, 717116122, 485961418, 615704083, 476049473, 354119987, 329471814, 620060202, 251964959, 45357250, 175414082, 671119137, 48735782, 122378970, 717506435, 18459328, 949577729, 771970076, 635808197, 608040366, 165916428, 258536202, 902229110, 617090616, 548564593, 613394864, 753777984, 577888302, 416452176, 881599549, 524547188, 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862659890, 801835044, 944139555, 886007778, 157956500, 184244219, 861459587, 574624180, 370500720, 439011802, 612771841, 826504956, 250048700, 463263393, 952614923, 996157958, 83807085, 368708002, 83937038, 643906175, 892744722, 781577692, 754447556, 391121651, 47625472, 494979565, 899365924, 855548156, 718245467, 758008976, 817972321, 269067909, 161074211, 589925302, 400244777, 647051601, 851189380, 942889223, 9983024, 428041294, 55302090, 456284567, 87730347, 485073493, 32117950, 243162170, 498593874, 2801117, 944619049, 613149643, 352773868, 177858867, 946106685, 787807764, 537376202, 611237536, 716787149, 13438606, 449606335, 201143145, 935269397, 833293382, 872198213, 823595689, 557500679, 975096990, 572907756, 790020244, 794585144, 39800114, 712117746, 602890874, 299572590, 253860034, 567822331, 692513972, 146600927, 380896458, 907990780, 772227106, 286621251, 748345506, 784733915, 412779987, 449429571, 461952211, 642834018, 270135381, 18378953, 486054845, 586104343, 273688550, 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495105329, 170582057, 403536153, 259681294, 31058776, 665921663, 365160621, 684208668, 148306231, 798600637, 136793270, 452757582, 390001574, 771292717, 469989356, 172053465, 827272350, 972060957, 881301574, 274052954, 919610927, 101995245, 801757510, 840771103, 420396591, 850350909, 935472223, 407873151, 486396318, 836617611, 398103002, 497405924, 827322488, 221186557, 531919636, 501986460, 7027536, 995509573, 605836899, 540744020, 266708215, 999588969, 750139831, 757978807, 966288747, 391480030, 950470370, 615056133, 223123986, 590526301, 464356125, 904941119, 570420584, 824371064, 634292921, 325714292, 164161043, 139535646, 57823174, 877945524, 707641683, 627332400, 623616255, 792704112, 121080634, 598518301, 505029588, 738400574, 70534733, 75645991, 869319171, 267844169, 946704053, 311644663, 497144552, 126786109, 985776140, 626915266, 384748446, 661023467, 40406486, 494539700, 726298383, 841033028, 504018084, 149072221, 530425959, 34716080, 127817978, 599414752, 356028052, 909681592, 433193290, 254048582, 908684845, 318775130, 389515378, 383907348, 923619728, 112336385, 453126610, 827794543, 261153278, 164821861, 343889998, 570532412, 736922954, 393911853, 663097742, 616988718, 468222879, 914492036, 519091374, 533684859, 560868978, 636469794, 516749046, 571245568, 532279018, 954098975, 40233011, 400772660, 40429369, 151682975, 890815048, 679277743, 384526101, 249938251, 363041124, 532245218, 632425122, 763411118, 534273823, 805721900, 133087759, 205076193, 118257093, 521871417, 899798981, 825664086, 124177199, 496350416, 844825656, 103311149, 58348337, 81069041, 175797285, 436600954, 868554528, 970860765, 125710968, 457299745, 372272984, 168972719, 475576689, 613000835, 369464458, 213878667, 678176690, 868915977, 965249043, 266788473, 593840838, 41234964, 277420681, 95009131, 533837096, 189808293, 869801057, 595120193, 228225365, 12135959, 416716523, 141657995, 451821421, 829745481, 855565272, 12945607, 192614757, 645781802, 399191777, 341683574, 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def ncr(n, r, k):
	su = 0
	for i in range(k, r + 1):
		su += facts[n] * invfacts[i] * invfacts[n - i] % mod
	return su % mod
for t in range(int(input())):
	n = int(input())
	arr = list(map(int, input().split()))
	arr.sort()
	s = pow(2, n - 1, mod)
	(i, count) = (0, 1)
	while i < n - 1:
		if arr[i] == arr[i + 1]:
			count += 1
		elif count > 1:
			for it in range(2, count + 1):
				s += ncr(n - it, i + 1 - it, i - count + 1)
			s %= mod
			count = 1
		i += 1
	if count > 1:
		for it in range(2, count + 1):
			s += ncr(n - it, i + 1 - it, i - count + 1)
	print(s % mod)


import math
import collections
import bisect
import heapq
import time
import itertools
import sys
from functools import reduce
import operator as op
memo = {}

def ncr(n, m):
	if m > n:
		return 0
	m = min(m, n - m)
	key = (n, m)
	if key in memo:
		return memo[key]
	ans = -1
	prekey = (n, m - 1)
	if prekey in memo:
		preval = memo[prekey]
		ans = preval * (n - m + 1) // m
	else:
		numer = reduce(op.mul, range(n, n - m, -1), 1)
		denom = reduce(op.mul, range(1, m + 1), 1)
		ans = numer // denom
	memo[key] = ans
	return ans
MOD = 10 ** 9 + 7

def solve(A):
	ans = 0
	A = list(sorted(collections.Counter(A).items()))
	N = len(A)
	if max([v[1] for v in A]) == 1:
		for i in range(1, N + 1, 2):
			ans += ncr(N, i)
			ans %= MOD
		return ans
	(left, right) = ([0] * (N + 1), [0] * (N + 1))
	for i in range(N):
		left[i + 1] = left[i] + A[i][1]
	for i in range(N - 1, -1, -1):
		right[i] = right[i + 1] + A[i][1]
	for (i, v) in enumerate(A):
		(l, m, r) = (left[i], v[1], right[i + 1])
		nrcs = [1] * (r + 1)
		for c in range(1, r + 1):
			nrcs[c] = nrcs[c - 1] + ncr(r, c)
		for b in range(1, m + 1):
			nb = ncr(m, b)
			for a in range(min(l, r + b - 1) + 1):
				mxc = min(a + b - 1, r)
				na = ncr(l, a)
				nc = nrcs[mxc] - (nrcs[a - b] if a - b >= 0 else 0)
				ans += na * nb * nc
				ans %= MOD
	return ans % MOD
T = int(input())
for ti in range(T):
	N = int(input())
	A = [int(x) for x in input().split()]
	print(solve(A))


import operator as op
from functools import reduce

def ncr(n, r):
	if r < 0 or r > n:
		return 0
	r = min(r, n - r)
	numer = reduce(op.mul, range(n, n - r, -1), 1)
	denom = reduce(op.mul, range(1, r + 1), 1)
	return numer // denom
for test in range(int(input())):
	n = int(input())
	mod = 1000000007
	res = 2 ** (n - 1) % mod
	l = [int(j) for j in input().split()]
	sor = sorted(l)
	for i in range(n):
		l = 0
		for j in range(i + 1, n):
			if sor[i] == sor[j]:
				l += 1
			else:
				break
		if l > 0:
			res += (ncr(n - 1, i + 1) - ncr(n - l - 1, i + 1)) % mod
		res = res % mod
	print(res % mod)


import bisect
mod = 10 ** 9 + 7
fact = [1]
for i in range(1, 2001):
	fact.append(fact[i - 1] * i)

def func1(right, left, freq):
	aa = left + right + freq
	ab = left + right
	val1 = fact[aa + 1] // (fact[left + 1] * fact[aa - left])
	val2 = fact[ab] // (fact[left + 1] * fact[ab - left - 1])
	return val1 - val2

def calc(aa, left, freq):
	val1 = fact[aa + 1] // (fact[left + 1] * fact[aa - left])
	sec = aa - freq
	val2 = fact[sec + 1] // (fact[left + 1] * fact[sec - left])
	return val1 - val2

def func2(right, left, freq):
	aa = left + right + freq
	nosf = right + freq - left + 1
	val1 = 0
	if nosf >= 0:
		val1 = calc(aa, left, nosf)
	start = min(freq + right, left - 1)
	fir = left + start
	las = right + left
	sum1 = fact[fir + 1] // (fact[start] * fact[fir + 1 - start])
	sum2 = fact[las] // (fact[right - 1] * fact[las - right + 1])
	return val1 + sum1 - sum2
for i in range(int(input())):
	a = int(input())
	v = list(map(int, input().split()))
	v.sort()
	hash = [False] * 2005
	for j in range(a):
		hash[v[j]] = True
	list1 = []
	sum1 = 0
	for j in range(a):
		x1 = bisect.bisect_right(v, v[j], 0, len(v))
		if x1 == j + 1:
			continue
		right = a - x1
		left = j
		freq = x1 - j - 2
		if right >= left:
			val = func1(right, left, freq)
		else:
			val = func2(right, left, freq)
		sum1 += val
	for j in range(a + 1):
		if j % 2 == 1:
			sum1 = (sum1 + fact[a] // (fact[j] * fact[a - j]) % mod) % mod
	print(sum1 % mod)


def generate_binfac_products():
	pList = [[0 for j in range(1000)] for i in range(1000)]
	for r in range(1, 500):
		for c in range(r, 999 - r):
			tmp = (pList[r][c - 1] + pList[r - 1][c] + 1) % 1000000007
			(pList[r][c], pList[c][r]) = (tmp, tmp)
	return pList

def calc_good_subseq():
	ctr = pow(2, N - 1, 1000000007)
	for i in range(N - 1):
		(preCtr, eqCtr, postCtr) = (i, 1, N - (i + 1))
		while postCtr and A[i + eqCtr] == A[i]:
			ctr += 1
			ctr += binFacList[preCtr][postCtr - 1]
			eqCtr += 1
			postCtr -= 1
	return str(ctr % 1000000007)
binFacList = generate_binfac_products()
T = int(input())
opList = []
for x in range(T):
	N = int(input())
	A = list(map(int, input().split()))
	A.sort()
	opList.append(calc_good_subseq())
print('\n'.join(opList))


from collections import defaultdict
from itertools import combinations
mod = 10 ** 9 + 7

def binomial(n, k):
	if 0 <= k <= n:
		(num, den) = (1, 1)
		for t in range(1, min(k, n - k) + 1):
			num *= n
			den *= t
			n -= 1
		return num // den % mod
	else:
		return 0

def sum_nC3(n):
	n += 1
	return binomial(n, 4)

def sum_nCr(n, r):
	n += 1
	return binomial(n, r + 1)

def brute():
	results = []
	for _ in range(1):
		A = [1] * 10 + [2] * 4 + [3] * 10 + [4] * 2 + [5] * 3
		A.sort()
		N = len(A)
		res = pow(2, N - 1, mod)
		if len(set(A)) != N:
			for i in range(2, N + 1, 2):
				for combi in combinations(A, i):
					if combi[i // 2 - 1] == combi[i // 2]:
						res += 1
		results.append(res)
	print('\n'.join((str(k) for k in results)))

def solve():
	results = []
	for _ in range(int(input())):
		N = int(input())
		arr = [int(k) for k in input().split()]
		arr.sort()
		freq = defaultdict(int)
		pos = dict()
		for i in range(N):
			freq[arr[i]] += 1
			if arr[i] not in pos:
				pos[arr[i]] = [i, 0]
			pos[arr[i]][1] = N - i - 1
		if len(freq) == N:
			results.append(pow(2, N - 1, mod))
			continue
		ans = pow(2, N - 1, mod)
		if len(freq) == 2 and 1 in freq.values():
			for x in range(max(freq.values()) - 1, 0, -1):
				ans = (ans + pow(2, x, mod) - 1) % mod
			results.append(ans)
			continue
		for (num, val) in freq.items():
			if val > 1:
				(left, right) = pos[num]
				for x1 in range(0, val - 1):
					ans = (ans + sum_nCr(right + left + val - 2, right + x1) - sum_nCr(right + left + x1 - 1, right + x1)) % mod
		results.append(ans)
	print('\n'.join((str(k) for k in results)))
solve()


from collections import Counter
from bisect import bisect

def make_pairs(l1, l2, n):
	(x, y, c, tot) = (0, 0, 0, 0)
	M = 10 ** 9 + 7
	las2_ind = bisect(l2, n - l1[0] - 2) - 1
	c = (las2_ind + 1) * (las2_ind + 2) // 2
	l1 = l1[0:las2_ind + 1]
	las2 = l2[las2_ind]
	xx = l1[0] + las2 + 1
	for i in l1:
		yy = i + 1
		tot = tot % M + ncr(xx, yy, M)
	(zz1, zz2) = (ncr(l1[-1] + l2[0] + 1, l2[0], M), ncr(l1[0] + l2[0], l1[0], M))
	zz = zz2 - zz1
	tot += zz
	tot %= M
	return [tot, c]

def ncr(n, r, p):
	if n < r:
		return 0
	num = den = 1
	for i in range(r):
		num = num * (n - i) % p
		den = den * (i + 1) % p
	return num * pow(den, p - 2, p) % p
for _ in range(int(input())):
	M = 10 ** 9 + 7
	n = int(input())
	a = [int(x) for x in input().split()]
	a.sort()
	fre = dict(Counter(a))
	f = list(set(a))
	total = pow(2, n - 1, M)
	for x in f:
		ind = a.index(x)
		freq = fre[x]
		if freq >= 2:
			(min1, min2, max1, max2) = (ind, n - ind - freq, ind + freq - 2, n - ind - 2)
			(l1, l2) = (list(range(min1, max1 + 1)), list(range(min2, max2 + 1)))
			lis = make_pairs(l1, l2, n)
			(total, xx) = (total + lis[0], lis[1])
			total -= xx
			total = total % M + ncr(freq, 2, M)
	print(total % M)


p = 10 ** 9 + 7
import functools

def power(x, y, p=10 ** 9 + 7):
	res = 1
	x = x % p
	while y > 0:
		if y & 1 == 1:
			res = res * x % p
		y = y >> 1
		x = x * x % p
	return res

def ncr(n, r):
	if r > n:
		return 0
	else:
		r = min(r, n - r)
		a = functools.reduce(lambda x, y: x * y, range(n, n - r, -1), 1)
		b = functools.reduce(lambda x, y: x * y, range(1, r + 1), 1)
		return a // b

def sum(n, x, i):
	if x < 2:
		return 0
	a = ncr(n - x, i) % p - ncr(n - 1, x + i - 1) % p
	for j in range(1, x):
		a = (a + ncr(n - 1, i + j) % p) % p
	return a
t = int(input())
for i in range(t):
	n = int(input())
	inp = list(map(int, input().split()))
	ans = power(2, n - 1)
	inp.sort()
	count = []
	dist = []
	dist.append(inp[0])
	x = 1
	for j in range(1, n):
		if inp[j] == inp[j - 1]:
			x = x + 1
		else:
			dist.append(inp[j])
			count.append(x)
			x = 1
	count.append(x)
	h = 0
	s = 0
	for j in range(len(dist)):
		s = (s + sum(n, count[j], h)) % p
		h = h + count[j]
	ans = (ans + s) % p
	print(ans)