Solitaire Pyramid HD

The rules are simple in this variation of solitaire: clear the pyramid row-by-row by removing pairs of cards that add up to 13 (jacks are 11, queens are 12, and kings are 13 by themselves and don't require a pair). You can form pairs with any cards that do not have another card covering them, as well as use the leftover cards in the stock to pair off more cards in the pyramid. You can go through the stock a maximum of three times. Can you clear the pyramid all the way to the top? Advanced players can attempt the additional challenge of obtaining a "perfect game": clearing all the cards without a single redeal of the stock.