Alex enjoys playing a card game, Australian Solitaire. This game involves a special deck of playing cards, with 4 Aces and 100 of every other denomination (Kings, Queens, ... 2s). There are no suits in this deck. In Australian Solitaire, the player places $$$N$$$ $$$(1 \leq N \leq 20)$$$ cards in a line, without replacement.

A sequence of cards is considered $$$upside-down$$$ if it meets the following criteria:

1. The first card can be any rank.

2. The rank of any subsequent card must either be strictly greater than the rank of the previous card, OR an Ace.

The rank of the cards from smallest to largest is Ace, 2, 3, … King. How many $$$upside-down$$$ sequences of $$$N$$$ cards are there? Two sequences are considered the same if for each card in the sequence, the denomination/rank of the card is the same.

Output your answer mod $$$10^9 + 7$$$.