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=10**9+7
n=int(raw_input())
N=map(int,raw_input().split())
cnt=[0]*(2*10**5+1)
mul=1
f=0
for i in N:
    cnt[i]+=1
    mul*=i
    mul%=mod
for i in cnt:
    if i%2!=0:
        f=1
        break
if f:
    mul2=1
    for i in cnt:
        mul2*=(i+1)
    print pow(mul,mul2/2,mod)
else:
    mul=1
    mul2=1
    for i in range(1,len(cnt)):
        mul*=pow(i,cnt[i]/2)
        mul%=mod
        mul2*=(cnt[i]+1)
    print pow(mul,mul2,mod)


