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.
readInts=lambda: list(map(int, input().split()))

n=int(input())
a=readInts()
p={}
for b in a:
    p[b]=p.get(b,0)+1

MOD=10**9+7
ret=1;cnt=1;
for x in p.items():
    t=x[1]
    now=pow(x[0],(1+t)*t//2,MOD)
    ret*=pow(ret,t,MOD)
    ret%=MOD
    ret*=pow(now,cnt,MOD)
    ret%=MOD
    cnt=cnt*(t+1)
    cnt%=MOD-1
    
print(ret)


