CF615D.Multipliers

Ayrat has number $n$ , represented as it's prime factorization $p_{i}$ of size $m$ , i.e. $n=p_{1}·p_{2}·...·p_{m}$ . Ayrat got secret information that that the product of all divisors of $n$ taken modulo $10^{9}+7$ is the password to the secret data base. Now he wants to calculate this value.

The first line of the input contains a single integer $m$ ( $1<=m<=200000$ ) — the number of primes in factorization of $n$ .

The second line contains $m$ primes numbers $p_{i}$ ( $2<=p_{i}<=200000$ ).

Print one integer — the product of all divisors of $n$ modulo $10^{9}+7$ .

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 $12$ . $1·2·3·4·6·12=1728$ .