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.
# Contest: 21 - Codeforces Rating >= 2200 (https://a2oj.com/ladder?ID=21)
# Problem: (27) Multipliers (Difficulty: 5) (http://codeforces.com/problemset/problem/615/D)

def rint():
    return int(input())


def rints():
    return list(map(int, input().split()))


from itertools import groupby
from functools import reduce
MOD = 10**9 + 7
n, p = rint(), sorted(rints())
p2 = ((k, sum(1 for _ in g)) for k, g in groupby(p))
res, numdivs = reduce(lambda t1, t2: (pow(t1[0], t2[1] + 1, MOD) * pow(t2[0], (t2[1] * (t2[1] + 1) // 2 * t1[1]) % (MOD - 1), MOD) % MOD, t1[1] * (t2[1] + 1) % (MOD - 1)), p2, (1, 1))
print(res)
