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Default A week of dates and counting them using the COUNTIF function with contingencies

=COUNTIF(Contact_Date,"="&DATE(2007,3,18)-
COUNTIF(Contact_Date,"<="&DATE(2007,3,24)))

The above is the formula I am attempting to use.

Definitions:

Contact_Date is a list of dates that range over 2000 cells that could
span up to 1 year.

In the example above I am wanting to find any dates that range between
and include the dates: 3.18.2007 and 3.24.2007

Problem:

The formula I am using is wanting to look past the dates provided and
count any prior dates that do not fall within the specified range. I
do not know why or how to fix it.

Any ideas?

In case the formula is seen as html here it is spelled out:
=COUNTIF(Contact_Date,"Greater than="&DATE(2007,3,18)-
COUNTIF(Contact_Date,"Less than="&DATE(2007,3,24)))

 
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