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.
M = 1000000007


def mod_pow(base, exp, mod):
    rst = 1
    while exp:
        if exp % 2:
            rst = (rst * base) % mod
        base, exp = (base * base) % mod, exp // 2
    return rst

primes = {}
raw_input()
for p in raw_input().split():
    primes[int(p)] = primes.get(int(p), 0) + 1

mul = 1
div_2 = True
for p, e in primes.items():
    if div_2 and e % 2:
        mul = (mul * (e+1) / 2) % (M-1)
        div_2 = False
    else:
        mul = (mul * (e+1)) % (M-1)

rst = 1
for p, e in primes.items():
    if div_2:
        count = (mul * e / 2) % (M - 1)
    else:
        count = (mul * e) % (M - 1)
    rst = (rst * mod_pow(p, count, M)) % M

print(rst)
