implement the chinese remainder theorem in python

chinese.py

def extended_euclidean(a, b):
    if a == 0:
        return b, 0, 1
    else:
        g, x, y = extended_euclidean(b % a, a)
        return g, y - (b // a) * x, x

def chinese_remainder(n, a):
    sum = 0
    prod = 1
    for ni in n:
        prod *= ni

    for ni, ai in zip(n, a):
        p = prod // ni
        g, x, y = extended_euclidean(p, ni)
        if g != 1:
            raise Exception('Moduli are not coprime')
        else:
            sum += ai * y * p
    return sum % prod

n = [3, 5, 7]
a = [2, 3, 2]
print(chinese_remainder(n, a))  # Output: 23