Multipliers

2000ms

262144K

Description:

Ayrat has number n, represented as it's prime factorization p_i of size m, i.e. n = p₁·p₂·...·p_m. 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 p_i (2 ≤ p_i ≤ 200 000).

Output:

Print one integer — the product of all divisors of n modulo 10⁹ + 7.

Sample Input:

2
2 3

Sample Output:

Sample Input:

3
2 3 2

Sample Output:

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.

Informação

Provedor Codeforces

Código CF615D