Strong Numbers

An integer is called strong if it's decimal representation $\overline { { a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 } }$ satisfies ${ a }_{ i }<{ a }_{ i+1 }$ if $a_i$ is odd and ${ a }_{ i }>{ a }_{ i+1 }$ if $a_i$ is even.

How many 4 digit strong numbers exist?

Bonus: how many 4 digit strong numbers have distinct digits?

Note: $\overline { { a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 } }$ denotes concatenation and $\overline { { a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 } } = 1000{ a }_{ 1 } + 100{ a }_{ 2 }+10{ a }_{ 3 }+{ a }_{ 4 }$