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

n = input()
primes = map(int, raw_input().strip().split())

f = {}
for p in primes:
    try: f[p] += 1
    except: f[p] = 1

isperf = 1
tau = 1
for p in f:
    e = f[p]
    if (e + 1) % 2 == 0 and isperf == 1:
        tau = tau * ((e + 1) // 2)
        isperf = 0
    else:
        tau = tau * (e + 1)

    if tau >= MOD2: tau %= MOD1

n = 1
if isperf:
    for p in f:
        e = f[p] // 2
        n = n * pow(p, e, MOD)
        if n >= MOD2: n %= MOD
else:
    for p in f:
        e = f[p]
        n = n * pow(p, e, MOD)
        if n >= MOD2: n %= MOD

ans = pow(n, tau, MOD)
print ans