mysql - GROUP BY で重複を削除するクエリ

Question

id_specific_price    id_product  
-------------------------------
            1                2  
            2                2  
            3                2  
            4                3  
            5                3  
            6                3  
            7                3

重複を削除する必要があり、期待される結果:

id_specific_price    id_product  
-------------------------------
            3                2  
            7                3

---

SELECT * 
  FROM ps_specific_price 
 WHERE id_specific_price NOT IN 
 (SELECT MAX(id_specific_price) 
    FROM ps_specific_price 
   GROUP BY id_product) 

動作しますが

DELETE FROM ps_specific_price 
 WHERE id_specific_price NOT IN 
(SELECT MAX(id_specific_price) 
   FROM ps_specific_price 
  GROUP BY id_product)

ではない。これを回避する例はたくさんありますが、何らかの理由で適応できません。GROUP BYだと思います。例えば：

DELETE FROM ps_specific_price 
 WHERE id_specific_price NOT IN
 (SELECT MAX(p.id_specific_price) 
    FROM (SELECT * FROM ps_specific_price ) as p)
   GROUP BY id_product

ここでどこが間違っていたのですか？