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 \(\overline { { a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 } } = 1000{ a }_{ 1 } + 100{ a }_{ 2 }+10{ a }_{ 3 }+{ a }_{ 4 }\)
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