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 = pow(10, 9) + 7
MOD1 = MOD - 1
MOD2 = MOD * MOD

m = input()
pri = map(int, raw_input().strip().split())

f = [0 for i in xrange(200002)]
for pr in pri: f[pr] += 1

primes = []
for i in xrange(200002):
    if f[i]: primes.append([i, f[i]])

exp = 1
k = 0
for p, e in primes:
    cur = e + 1
    while cur % 2 == 0:
        cur //= 2
        k += 1
    exp = exp * cur
    if exp >= MOD2: exp %= MOD1

ans = 1
for p, e in primes:
    nk = k
    if e % 2 == 0: e >>= 1
    else: nk -= 1
    cexp = exp * pow(2, nk, MOD1) * e % MOD1
    ans = ans * pow(p, cexp, MOD) % MOD

print ans