def solve(c):
    # By sorting the cards, we ensure that we handle the smallest constraints first, which simplifies checking validity and calculating permutations
    c.sort()

    result = 1

    for i in range(len(c)):

        # For each card at index i, the value must be at most i. If any card's value exceeds its index, it can't be placed in a valid position, resulting in 0 permutations
        if c[i] > i:
            return 0

        # Permutations Calculation: For each valid card, the number of available positions is determined by (i + 1 - c[i]), where i is the index (0-based). The product of these values for all cards gives the total number of valid permutations
        result = (result * (i + 1 - c[i])) % 1000000007

    return result

cnt, mod = [0] * max(len(c), max(c)+1), 1000000007
for i in c: cnt[i]+=1
return math.prod(x-i for i,x in enumerate(accumulate(cnt)))%mod

def solve(c):
    lyl = []
    c.sort(reverse=True)
    ii = 0
    n = len(c)
    prod = 1
    for i in c:
        if i < n:
            prod *= (n - i - ii)
        else:
            return 0
        ii += 1
    return prod % 1000000007