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.
MOD = 10 ** 9 + 7
ans = 1
tau = 1
N = 200005
cnt = [0] * N

n = int(input())
for x in input().split() :
	cnt[int(x)] += 1

for i in range(1, N) :
	if cnt[i] == 0 : continue
	ans = pow (ans, cnt[i] + 1, MOD) * pow (i, cnt[i] * (cnt[i] + 1) // 2 % (MOD - 1) * tau % (MOD - 1), MOD) % MOD
	tau = tau * (cnt[i] + 1) % (MOD - 1)

print (ans)