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(raw_input())
M=(10**9+7) 
pr=map(int,raw_input().split())
d={}
ans=1
for i in xrange(0,n):
    ans=(ans*pr[i])%M
    if pr[i] in d:
        d[pr[i]]=d[pr[i]]+1
        
    else:
        d[pr[i]]=1
b=1
ans=1
def mod_pow(base, exp, mod):
    rst = 1
    while exp:
        if exp % 2:
            rst = (rst * base) % mod
        base, exp = (base * base) % mod, exp // 2
    return rst
#print d        
for k in d:
    b=b*(d[k]+1)
    #ans=(ans%M*(k**d[k])%M)%M
#print b
#print d    
for k in d:
    #print k,d[k],b
    m=(d[k]*b)/2
    m=m%(M-1)
    #print m
    ans=ans*(mod_pow(k,m,M))%M
    #print ans
print ans%M 
#print ans   