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.
from sys import stdin

m = int(stdin.readline())

p = [int(x) for x in stdin.readline().split()]

pD = {}

for x in p:
    if x in pD:
        pD[x] += 1
    else:
        pD[x] = 1

perms = 1

for x in pD:
    perms *= pD[x]+1
    perms %= 1000000006*2

prod = 1

for x in pD:
    prod *= pow(x,perms*pD[x]//2,1000000007)
    prod %= 1000000007
print(prod%1000000007)
