# 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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