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())
s = input().split()
m = [-1]
ch = 1
md = 1000000007
for i in range(n):
    m.append(int(s[i]))
    ch = (ch*int(s[i])) % md
m.sort()
kol = 1
z = 1
kolraz = 0
fl = 1
sq = 1
for i in range(2, n+1):
    if m[i] == m[i-1]:
        kol += 1
    else:
        for j in range(kol//2):
            sq = (sq * m[i-1]) % md
        if kol % 2 == 1:
            fl = 0
        z *= (kol+1)
        kol = 1
        kolraz += 1
z *= (kol+1)
for j in range(kol//2):
    sq = (sq * m[n]) % md
if kol % 2 == 1:
    fl = 0
res = 1
kol = z
kol //= 2
if fl:
    res = sq
while kol:
    if kol & 1:
        res = (res*ch) % 1000000007
    ch = (ch*ch) % md
    kol >>= 1
print(res)
