Counting the number of people on leave per month

Book1.xlsx
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I'm looking for a formula that can give me the count of leave per month in column F considering the leave start durations in column B and leave end in column C

the formula should ignore the blank cell as well the cells that ara contains text or anything else apart from date format

I hope I can find the solution to this inquiry.

I have already attached the template for your reference.

@tanasedn thank you so much for their brilliant job, much appreciated.

@tanasedn sorry to bother you, but it's possible to add one more condition to this formula!!

I need the formula to be able also to fitch the same result but in the additional condition that is in the drop-down list @ "F1"

in that way ill be able to filter the people on leave per month but for a specific group

much appreciated if this can be possible

I look forward to hearing back from you.

I have attached the updated worksheet again for reference

Book1 (5).xlsx

@tanasedn brilliant result, thank you so much, worked great