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CREATE TABLE `s` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `c1` int(11) NOT NULL,
  PRIMARY KEY (`id`),
  KEY `c1` (`c1`)) ;

INSERT INTO `s` VALUES (1,1),(2,1),(122,1),(123,1),(212,61),(213,62);

SELECT count(id) FROM a  
WHERE id IN ( SELECT a1.id   FROM a a1  JOIN b ON a1.id = b.id  JOIN s  ON b.c1 =  s.id   WHERE s.c1=61);

SELECT count(id) FROM a use index(PRIMARY)
 WHERE id IN ( SELECT a1.id   FROM a a1  JOIN b ON a1.id = b.id  JOIN s  ON b.c1 =  s.id   WHERE s.c1=61);

