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.


n = int(input())
exps = {}
for x in [ int(x) for x in input().split() ]:
	exps[x] = exps.get(x,0)+1
r,m = 1,1
M = 1000000007
P = M-1
for p,e in exps.items():
	E = (e*(e+1)//2)%P 
	E = E*m%P
	r = pow(r,e+1,M)*pow(p,E,M)%M
	m = m*(e+1)%P
print(r)


# C:\Users\Usuario\HOME2\Programacion\ACM