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.
#!/usr/bin/env python3
import math
lca = lambda a, b: a * b // math.gcd(a,b)
mod = 1000000007
m = int(input())
ps = map(int,input().split())
cnt = {}
for p in ps:
    if p not in cnt:
        cnt[p] = 0
    cnt[p] += 1
lca_i = 1
k = 1
for i in cnt.values():
    k *= i + 1
    lca_i = lca(lca_i, i+1)
ans = 1
for p, i in cnt.items():
    ans = ans * pow(p, i*(i+1)//2 * lca_i//(i+1), mod) % mod
ans = pow(ans, k//lca_i, mod)
print(ans)
