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.
def binaryPow(a, q, mod):
    a %= mod
    if q == 0:
        return 1
    elif q % 2 == 1:
        return (a * binaryPow(a * a, q // 2,  mod)) % mod
    else:
        return binaryPow(a * a, q // 2,  mod) %  mod

 
mod = 1000000007
n = int(input())
gg = [int(a) for a in input().split()]
fact = {}
for i in range(n):
    if gg[i] not in fact.keys():
        fact[gg[i]] = 1
    else:
        fact[gg[i]] += 1
d = 1
ans = 1
for k, v in fact.items():
    tmp = binaryPow(k, (v + 1) * v // 2, mod)
    ans = binaryPow(ans, (v + 1), mod) * binaryPow(tmp, d, mod) % mod
    d = d * (v + 1) % (mod - 1)
print(ans)