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())
MOD = 10**9 + 7
p = [int(i) for i in input().split()]
p.sort()
a = []
index = 0
now = p[0]
cnt_now = 0
while (index < n):
    while (index < n and p[index] == now):
        index += 1
        cnt_now += 1
    a.append([now, cnt_now])
    if index < n:
        now = p[index]
        cnt_now = 0
tau = 1
ans = 1
for i in range(len(a)):
    tau = tau * (a[i][1] + 1)
for i in range(len(a)):
    deg = ((tau * a[i][1]) // 2)
    ans = (ans * pow(a[i][0], deg % (MOD - 1), MOD)) % MOD
print(ans)