Ayrat has number n, represented as it's prime factorization pi of size m, i.e. n = p1·p2·...·pm. Ayrat got secret information that that the product of all divisors of n taken modulo 109 + 7 is the password to the secret data base. Now he wants to calculate this value.

Input

The first line of the input contains a single integer m (1 ≤ m ≤ 200 000) — the number of primes in factorization of n. 

The second line contains m primes numbers pi (2 ≤ pi ≤ 200 000).

Output

Print one integer — the product of all divisors of n modulo 109 + 7.

Examples

Input

2
2 3


Output

36


Input

3
2 3 2


Output

1728

Note

In the first sample n = 2·3 = 6. The divisors of 6 are 1, 2, 3 and 6, their product is equal to 1·2·3·6 = 36.

In the second sample 2·3·2 = 12. The divisors of 12 are 1, 2, 3, 4, 6 and 12. 1·2·3·4·6·12 = 1728.
N = 202020
M = 1000000007
n = int(raw_input())
x = [int(s) for s in raw_input().split(" ")]
t = 1
k = 1
c = [0]*202020
for u in x:
	c[u] += 1
for i in range(1,N):
	if c[i] == 0:
		continue
	z = 1
	t2 = 1
	k2 = 0
	for j in range(c[i]):
		z *= i
		z %= M
		t2 *= t*pow(z,k,M)
		k2 += k
		t2 %= M
	t *= t2
	k = k+k2
	k %= (M-1)
	t %= M
print t
