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.
n = int(input())
l = list(map(int, input().split()))
M = int(1e9+7)
counter = {}
num = 1
for elem in l:
    num = (num * elem) % M
    try:
        counter[elem]+=1
    except:
        counter[elem] = 2
        
d = 1
for elem in counter:
    d *= counter[elem]
    
res = pow(num, d//2, M)
checkodd = 1
for elem in counter:
    if counter[elem] % 2 == 0: 
        checkodd = 0
        break
if checkodd:
    for elem in counter:
        for i in range(counter[elem] // 2):
            res = (res * elem) % M
            
print(res)