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.
import sys

M = int(input())
P0 = list(map(int, input().split()))
P0 = sorted(P0)
P = []
Q = []
temp = 0
for i in range(M):
    if(temp != P0[i]):
        temp = P0[i]
        P.append(temp)
        Q.append(1)
    else:
        Q[len(Q)-1] += 1
mod = 10**9 + 7
M = len(Q)

T = [1] * M
T1 = [1] * (M + 1)
T2 = [1] * (M + 1)
for i in range(M):
    T[i] = ((Q[i] * (Q[i] + 1)) // 2) % (mod - 1)
    T1[i+1] = (T1[i] * (Q[i] + 1)) % (mod - 1)
    T2[M - i - 1] = (T2[M - i] * (Q[M - i - 1] + 1)) % (mod - 1)
ans = 1
for i in range(M):
    temp = pow(P[i], T[i], mod)
    t = (T1[i] * T2[i + 1]) % (mod - 1)
    a = pow(temp, t, mod)
    ans = (ans * a) % mod
print(ans)