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 sys

#Library Info(ACL for Python/Pypy) -> https://github.com/not522/ac-library-python

def input():
    return sys.stdin.readline().rstrip()

DXY = [(0, -1), (1,0), (0, 1), (-1,0)] #L,D,R,Uの順番

mod = int(1e9 + 7)
from collections import defaultdict

def main():
    n = int(input())    
    d = defaultdict(int)    
    a = list(map(int,input().split()))
    for v in a:d[v] += 1

    group_product = 1
    group_size = 1 # modulo mod - 1
    

    for p,ord in d.items():
        group_product = pow(group_product,ord + 1,mod)
        group_product *= pow(p,ord * (ord + 1) // 2 * group_size,mod)
        group_product %= mod
        group_size *= (ord + 1)        
        group_size %= (mod - 1)

    print(group_product % mod)
    return 0


if __name__ == "__main__":
    main()
