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