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.
import functools, operator
m = int(input())
p = [int(x) for x in input().split()]
P = {}
n = 1
for i in p:
    P[i] = P.get(i, 0) + 1
    n = n * i % 1000000007
dv = functools.reduce(operator.mul, (l + 1 for l in P.values()))
prod = 0;
#n = functools.reduce(operator.mul, (pow(p,i,1000000007) for p,i in P.items()))
if dv & 1:
    #prod = pow(int(n**0.5), dv, 1000000007)
    prod = pow(int(functools.reduce(operator.mul, (pow(p,i//2,1000000007) for p,i in P.items()))), dv, 1000000007)
    #prod = pow(int(n**0.5), dv, 1000000007);
else:
    #prod = pow(n, dv//2, 1000000007)
    #prod = pow(functools.reduce(operator.mul, p), dv//2, 1000000007)
    prod = pow(n, dv//2, 1000000007)
print(prod % 1000000007)

