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.
M = 1000000007


def mpow(n, p):
    if p == 0:
        return 1

    ans = mpow(n, int(p / 2))
    ans = (ans * ans) % M

    if p % 2 == 1:
        ans = ans * n

    return ans % M


n = int(input())
arr = input().split(' ')

m = [0] * 200001

for i in arr:
    m[int(i)] = m[int(i)] + 1

d = 1

ans1 = 1
ans2 = 1
e = -1

for i in m:
    e += 1
    if i == 0:
        continue
    if i % 2 == 0:
        ans1 = (ans1 * mpow(e, i / 2)) % M
    else:
        ans2 = (ans2 * mpow(e, i)) % M

b = False

for i in m:
    ans1 = mpow(ans1, i + 1) % M
    if i % 2 == 1:
        if not b:
            ans2 = mpow(ans2, (i + 1) / 2) % M
        else:
            ans2 = mpow(ans2, i + 1) % M
        b = True
    else:
        ans2 = mpow(ans2, i + 1) % M

print((ans1 * ans2) % M)