list consecutive intervals and calculate covered minutes, MySQL

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drop table if exists contracts;
create table contracts (employee_id int, start_date datetime, end_date datetime);

INSERT INTO contracts (employee_id,start_date,end_date) 
VALUES 
(666, '2010-01-01', '2013-01-01 07:13:15'), 
(666, '2013-01-01 07:13:15', '2013-05-01 12:30:01'), 
(666, '2013-05-01 12:30:01', '2013-10-11'),
(777, '2012-01-11', '2013-03-02'),
(777, '2013-03-02', '2014-07-15'),
(777, '2015-01-15', '2015-05-20');

SELECT 
c.employee_id
,MIN(c.start_date) AS start_date
,MAX(c.end_date) AS end_date
,COUNT(*) AS numcontracts,
TIMESTAMPDIFF(minute,MIN(c.start_date),MAX(c.end_date)) AS timediff
FROM 
(
        SELECT 
        c0.*
        ,(@rn := @rn + COALESCE(startflag, 0)) AS cumestarts
        FROM 
        (SELECT c1.*,
                 (NOT EXISTS (SELECT 1
                      FROM contracts c2
                      WHERE c1.employee_id = c2.employee_id AND
                        c1.start_date = c2.end_date
                     )
                 ) AS startflag
              FROM contracts c1
              ORDER BY employee_id, start_date

) c0 CROSS JOIN (SELECT @rn := 0) params

) c
GROUP BY c.employee_id, c.cumestarts


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