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
P = [0] * 200001

m = input()
ps = map(int, raw_input().split())
for p in ps:
    P[p] += 1
ans = count = 1
for p, e in enumerate(P):
    if e:
        tmp = 1
        prev = ans
        next_ans = 1
        pp = pow(p, count, MOD)
        for i in xrange(e+1):
            next_ans *= tmp * prev
            next_ans %= MOD
            tmp *= pp
            tmp %= MOD
        count *= (e + 1)
        count %= MOD*MOD-1
        ans = next_ans
print ans
