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.
mod = 1000000000+7
def power(a,n):
    if a==0 :
        return 0
    if n==0:
        return 1
    if n==1 :
        return a
    ans = power(a,n/2)
    ans = ans *ans %mod
    if n%2 :
        ans = ans *a %mod
    return ans

n = int(raw_input())
p = map(int,raw_input().split())
p = sorted(p)

final = 1
for x in p:
    final = final * x %mod
count = 1
m = 1

ret = 1
for i in xrange(n-1):
    if p[i] == p[i+1]:
        count += 1
    else :
        m = m *(count+1)
        if count %2 == 0:
            ret = ret * pow(p[i],count/2,mod)
        count = 1


m = m* (count +1)
ret = ret * pow(p[n-1], count / 2,mod)

if m %2 == 0:
    ret = 1
#print m,count
print pow(final,m/2,mod)*ret%mod
