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
m = input()
z = map(int, raw_input().split())
p = {}
cnt = 0
for x in z:
    p[x] = p.get(x, 0L) + 1 #get in dictionary

ans = 1L
ck = False
k = 1L
for x, y in p.items():
    if(y % 2 == 1):
        ck = True
        break

if ck:
    for x, y in p.items():
        ans = ans * long(pow(x, y, mod)) % mod
        if y % 2 == 1 and ck:
            k = k * (y + 1) / 2 % (mod - 1)
            ck = False
        else:
            k = k * (y + 1) % (mod - 1)
else:
    for x, y in p.items():
        ans = ans * pow(x, y/2, mod) % mod
        k = k * (y + 1) % (mod - 1)


print pow(ans, k, mod)