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 collections import Counter

MOD = 1000000007

def pow_m(base, pw):
    if pw == 0:
        return 1
    elif pw % 2 == 1:
        return (((pow_m(base, pw // 2) ** 2) % MOD) * base) % MOD
    else:
        return (pow_m(base, pw // 2) ** 2) % MOD

m = int(input())
p = [int(x) for x in input().split()]
c = Counter(p)

is_square = all(c[x] % 2 == 0 for x in c)

base, root, pw = 1, 1, 1
for elem in c:
    if is_square:
        ppw = pow_m(elem, c[elem] // 2)
        base = (base * ((ppw ** 2) % MOD)) % MOD
        root = (root * ppw) % MOD
    else:
        base = (base * pow_m(elem, c[elem])) % MOD
    pw *= c[elem] + 1
pw = (pw // 2) % (MOD - 1)

prod = pow_m(base, pw)
if is_square:
    prod = (prod * root) % MOD
print(prod)
