Multiple values when using IF function in Google Spreadsheet

I have a list of points that need to be assigned in to a certain tier. For example:

<1250 = Tier 1
1250-1650 = Tier 2
>1650 = Tier 3

I've been trying to use this formula:

=IF(AND(B2 > 0,B2 < 1250),"1",IF(AND(B2 > 1250,B2 < 1650),"2",IF(AND(B2 > 1650,B2 < 2000),"3")))

The problem is that when a value is 1250 "FALSE" is returned, I can't seem to figure out how to fix this. Any help would be much appreciated.

The sheet is here.