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 = int(input())
a = []
a = input().split()
ans = 1
mod = int(1e9 + 7)
def bin_pow(x, y) :
    res = x
    ret = 1
    while(y > 0) :
        if(y % 2) :
            ret = (ret * res) % mod
        res = (res * res) % mod
        y //= 2;
    return ret % mod
b = []
for i in range(200001) :
    b.append(0)
for i in range(m) :
    a[i] = int(a[i])
    b[a[i]] += 1
cnt = 1
for i in range(200001) :
    if b[i] != 0 :
        cnt = (cnt * (b[i] + 1)) % (2 * (mod - 1))
c = []
for i in range(200001) :
    c.append(0)
for i in range(m) :
    if c[a[i]] == 0 :
        ans = ans * bin_pow(a[i],(cnt * b[a[i]] / 2) % (2 * (mod - 1))) % mod
        c[a[i]] = 1
print(int(ans % mod))