CN-SMO 2006 Problem 3

There is a standard deck of $52$ cards without jokers. The deck consists of four suits(diamond, club, heart, spade) which include thirteen cards in each. For each suit, all thirteen cards are ranked from " $2$ " to " $A$ " (i.e. $2, 3,\ldots , Q, K, A$ ). A pair of cards is called a "straight flush" if these two cards belong to the same suit and their ranks are adjacent. Additionally, " $A$ " and " $2$ " are considered to be adjacent (i.e. "A" is also considered as " $1$ "). For example, spade $A$ and spade $2$ form a "straight flush"; diamond $10$ and diamond $Q$ are not a "straight flush" pair. Determine how many ways of picking thirteen cards out of the deck such that all ranks are included but no "straight flush" exists in them.