/* This outer query is  only for ordering by  project duration */
SELECT P3.sd,P3.ed FROM 

(SELECT  MIN(P1.Start_Date) AS sd  , P2.End_Date  AS ed
FROM Projects AS P1
INNER JOIN Projects AS P2
ON  p2.End_Date  NOT IN (SELECT Start_Date From Projects) /*we exclude the end dates that exists on Start_Date which means they are part of the same project*/
AND
/*Once we've found an end date  not same as any of the start dates we check backwards how many other cols  there are within the same time span  count them first if the number equals to the day difference that means they are actually linked.  Use "group by" End_date with MIN() to  find the earliest start date there is that is linked        */
(SELECT count(*) From Projects  WHERE Start_Date BETWEEN P1.Start_Date AND P2.End_Date ) = DATEDIFF(P2.End_Date,P1.Start_Date) 

GROUP BY P2.End_Date) AS P3


ORDER by DATEDIFF(P3.ed, P3.sd), P3.sd ;

WITH difference AS (
    SELECT 
        start_date, 
        end_date,
        @group := IF(@prev_end = start_date, @group, @group + 1) AS grp,
        @prev_end := end_date
    FROM projects, (SELECT @prev_end := NULL, @group := 0) vars
    ORDER BY 1
)
SELECT 
    MIN(start_date) AS start_date, 
    MAX(end_date) AS end_date
FROM difference
GROUP BY grp
ORDER BY count(grp), 1;

 select min(Start_Date), max(End_date)
 from (
    select *, day(End_date) - row_number() over (order by end_date) dif
    from Projects) x
group by dif
order by datediff(day,min(Start_Date), max(End_date)), min(Start_Date);

select start_date, end_date 
from 
(select start_date, row_number() over(order by start_date) as x from projects where start_date not in (select end_date from projects)) as a  join 

(select end_date, row_number() over(order by end_date) as y  from projects where end_date not in (select start_date from projects)) as b 
on a.x = b.y

order by datediff(end_date, start_date), 1