DAX script for measure based on date dimention

In SSAS I have the fact table:

and Date dimention:

...

There is no relationship between the fact table and Date dimention.

I need to create a measure with a unique count of ContractID, where Date value (Date dimention) between DateFrom and DateTo (fact table). The measure should work when choosing any date level from Date dimention: year, year-month, year-month-date.

CountOfContracts :=
CALCULATE(
           DISTINCTCOUNT('FactTable'[ContractId]),
           FILTER('FactTable',
                     (
                        SELECTEDVALUE('DateDimention'[Date]) >= 'FactTable'[DateFrom] &&
                        SELECTEDVALUE('DateDimention'[Date]) <= 'FactTable'[DateTo]
                     )
                  )
         )

Problem: this doesn't work with date at month and year level

Pieter, thanks for the advice, I was thinking of doing the same, but there is a risk of greatly increasing the size of the fact table. This is how I managed to solve the problem:

CountOfContracts :=
var MonthId = LOOKUPVALUE('DateDimention'[year_month_order/* format YYYYMM */],'DateDimention'[Year], SELECTEDVALUE('DateDimention'[Year]), 'DateDimention'[MonthId], SELECTEDVALUE('DateDimention'[MonthId]))
return
switch
(
    true,
    HASONEVALUE('DateDimention'[Year]) && not HASONEVALUE('DateDimention'[MonthId]),
                 CALCULATE(
                            DISTINCTCOUNT('FactTable'[ContractID]),
                FILTER('FactTable',
                (
                    SELECTEDVALUE('DateDimention'[Year]) >= year('FactTable'[DateFrom]) &&
                    SELECTEDVALUE('DateDimention'[Year]) <= year('FactTable'[DateTo])
                )
                      )
            ), 

                HASONEVALUE('DateDimention'[MonthId]) && not HASONEVALUE('DateDimention'[Date]),
        CALCULATE(
               DISTINCTCOUNT('FactTable'[ContractID]),
                FILTER('FactTable',
                (
                    MonthId >= year('FactTable'[StartDate])*100 + month('FactTable'[DateFrom]) &&
                    MonthId <= year('FactTable'[EndDate])*100 + month('FactTable'[DateTo])
                )
                )
            ),

        HASONEVALUE('DateDimention'[Date]),
        CALCULATE(
              DISTINCTCOUNT('FactTable'[ContractID]),
                FILTER('FactTable',
                (
                    SELECTEDVALUE('DateDimention'[Date]) >= 'FactTable'[DateFrom] &&
                    SELECTEDVALUE('DateDimention'[Date]) <= 'FactTable'[DateTo]
                )
                )
            ),

        BLANK()
)