Lemon Inc. had the following sales budgeted:

October $$200,000$

November $$340,000$

December $$320,000$

January $$180,000$

Lemon's collection pattern is $30\%$ in month of the sale, $50\%$ in month following the sale and $20\%$ in second month following the sale.

What is Lemon's budgeted cash collections for January?