Sum nested values with Linq

Simple problem: I have Users that can have many Orders that can have many Products. What does the Linq (lambda) query look like to get a User's grand total of all Product.Price values?

I've tried this:

int total = users.Sum(u => u.Orders.Sum(o => o.Products.Sum(p => p.Price)));

But it's giving me:

The cast to value type 'I开发者_Go百科nt32' failed because the materialized value is null. Either the result type's generic parameter or the query must use a nullable type.

Of course, a user may not have any orders, and an order may not have any products. But Product.Price is not a nullable value.

So I tried this, thinking it was choking on empty collections:

int total = users.Sum(u => u.Orders.Sum(o => o.Products.Sum(p => p.Price) ?? 0) ?? 0) ?? 0;

But it's throwing compile errors, saying the left side of the ?? is not nullable.

What am I doing wrong?

Thanks in advance.

UPDATE: A working version of my examples above after using Marc's logic from his answer:

int total = users.Sum(u => u.Orders.Sum(o => o.Products.Sum(p => (int?)p.Price))) ?? 0;

int total = (from user in users
             from order in user.Orders
             from product in order.Products
             select (int?)product.Price).Sum() ?? 0;

would be my offering; there is an annoying glitch that the SUM in SQL over 0 rows is NULL, not 0 - the above works around that.

or as lambdas (from comments):

int total = users.SelectMany(user => user.Orders)
                 .SelectMany(order => order.Products)
                 .Sum(product => (int?)product.Price) ?? 0;