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.
MOD = 1000000007
top = 0
t = [0] * 200005
x = int(input())
y = list(map(int, input().split(' ')))

if 10**9+7 in y:
    print(0)
    quit()

base = 1

sq = True

for i in y:
    t[i] += 1
    base *= i
    base %= MOD

for i in range(200005):
    if (t[i] % 2 == 1):
        sq = False

ans = 1
powf = 1
if sq:
    for i in range(200005):
        ans *= pow(i, t[i]//2, MOD)
        ans %= MOD
        powf *= (t[i] + 1)
        powf %= (MOD - 1)
    print(pow(ans, powf, MOD))
    quit()

two = False
for i in range(200005):
    if (not two and t[i] % 2 == 1):
        two = True
        powf *= (t[i]+1)//2
    else:
        powf *= (t[i]+1)
    powf %= (MOD - 1)

print(pow(base, powf, 10**9+7))
