Select First Row In Each Group MySQL

SELECT  
      MIN(purchases2.id),  # change to MAX if you want the highest value
      purchases1.customer, 
      purchases1.total
FROM 
    PURCHASES purchases1
    JOIN (SELECT p.customer,
                 MAX(total) AS max_total
            FROM PURCHASES purchases
            GROUP BY p.customer) purchases2 
   ON purchases2.customer = purchases1.customer
      AND purchases2.max_total = purchases1.total
GROUP BY purchases1.customer, purchases1.total
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