Total number of increasing functions

How many strictly increasing functions ff are possible such that f:ABf:A \rightarrow B, where A={a1,a2,a3,a4,a5,a6}A=\{ a_1,a_2,a_3,a_4,a_5,a_6\} , and B={1,2,3,4,5,6,7,8,9}B=\{ 1,2,3,4,5,6,7,8,9\} and ai+1>aiiNa_{i+1}>a_i \forall i \in \mathbb{N} and f(ai)i f( a_i) \neq i ?


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