SELECT 
    T1.Start_Date,
    T2.End_Date
FROM (
    SELECT ROW_NUMBER() OVER (ORDER BY Start_Date ASC) AS r,
    Start_Date
    FROM Projects
    WHERE (Start_Date NOT IN (SELECT End_Date FROM Projects))
) AS T1
LEFT JOIN 
    (SELECT ROW_NUMBER() OVER (ORDER BY End_Date ASC) AS r,
    End_Date
    FROM Projects
    WHERE (End_Date NOT IN (SELECT Start_Date FROM Projects))
) AS T2 ON T1.r=T2.r
ORDER BY DATEDIFF(T2.End_Date, T1.Start_Date) ASC, T1.Start_Date ASC

-- Select the unmatched Start_Date and End_Date pairs
SELECT 
    T1.Start_Date,     -- Start date of a project (not matched to any end date)
    T2.End_Date        -- End date of a project (not matched to any start date)
FROM (
    -- Subquery T1: Get all Start_Dates that are not listed as End_Dates
    SELECT 
        ROW_NUMBER() OVER (ORDER BY Start_Date ASC) AS r,  -- Assign a row number for matching
        Start_Date
    FROM Projects
    WHERE Start_Date NOT IN (SELECT End_Date FROM Projects)  -- Filter: unmatched start dates
) AS T1

-- LEFT JOIN to match each unmatched Start_Date with an unmatched End_Date
LEFT JOIN (
    -- Subquery T2: Get all End_Dates that are not listed as Start_Dates
    SELECT 
        ROW_NUMBER() OVER (ORDER BY End_Date ASC) AS r,  -- Assign a row number for matching
        End_Date
    FROM Projects
    WHERE End_Date NOT IN (SELECT Start_Date FROM Projects)  -- Filter: unmatched end dates
) AS T2 
ON T1.r = T2.r  -- Join rows by row number (to pair start and end dates in order)

-- Order results by shortest duration first, then by Start_Date
ORDER BY 
    DATEDIFF(T2.End_Date, T1.Start_Date) ASC,  -- Sort by number of days between Start and End
    T1.Start_Date ASC;