615_D. Multipliers
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.
```python
MD = 1000000007
m = int(input())
p = list(map(int, input().split()))
q = {}
for el in p:
    if el in q:
        q[el] += 1
    else:
        q[el] = 2
sum1 = 1
sum2 = 1
for el in q:
    sum1=sum1*q[el]
    sum2=sum2*pow(el,(q[el]-1),MD)
sum=pow(sum2,sum1//2,MD)
if sum1 % 2 == 1:
    for el in q:
        sum = (sum * pow(el,q[el]//2,MD)) % MD
print(sum)
```