Question: For how many seasons was the producer of Rainbow a judge on American Idol?

full_context: Document 1: Through the Rain: "Through the Rain" is a song by American singer Mariah Carey, taken from her ninth studio album, "Charmbracelet" (2002). It was written by Carey and Lionel Cole, and produced by the former and Jimmy Jam and Terry Lewis. The song was released as the album's lead single on October 17, 2002, and a shorter version was used as the ending credits theme for a 2002 Japanese drama known as "You're Under Arrest". Classified by Carey as a ballad, it is influenced by R&B music genres, and features a simple and under-stated piano melody, backed by soft electronic synthesizers. "Through the Rain" was meant to be an insight into Carey personal struggles throughout 2001, and lyrically talks about encouraging others.
Document 2: American Idol: Season 12 premiered on January 16, 2013. Judges Jennifer Lopez and Steven Tyler left the show after two seasons. This season's judging panel consisted of Randy Jackson, along with Mariah Carey, Keith Urban and Nicki Minaj. This was the first season since season nine to have four judges on the panel. The pre-season buzz and the early episodes of the show were dominated by the feud between the judges Minaj and Carey after a video of their dispute was leaked to TMZ.
Document 3: American Idol: Towards the end of the season, Randy Jackson, the last remaining of the original judges, announced that he would no longer serve as a judge to pursue other business ventures. Both judges Mariah Carey and Nicki Minaj also decided to leave after one season to focus on their music careers.
Document 4: American Idol: The show had originally planned on having four judges following the Pop Idol format; however, only three judges had been found by the time of the audition round in the first season, namely Randy Jackson, Paula Abdul and Simon Cowell. A fourth judge, radio DJ Stryker, was originally chosen but he dropped out citing "image concerns". In the second season, New York radio personality Angie Martinez had been hired as a fourth judge but withdrew only after a few days of auditions due to not being comfortable with giving out criticism. The show decided to continue with the three judges format until season eight. All three original judges stayed on the judging panel for eight seasons.
Document 5: American Idol: The thirteenth season premiered on January 15, 2014, with Ryan Seacrest returning as host. Randy Jackson and Keith Urban returned, though Jackson moved from the judging panel to the role of in-mentor. Mariah Carey and Nicki Minaj left the panel after one season. Former judge Jennifer Lopez and former mentor Harry Connick, Jr. joined Urban on the panel. Also, Nigel Lythgoe and Ken Warwick were replaced as executive producers by Per Blankens, Jesse Ignjatovic and Evan Pragger. Bill DeRonde replaced Warwick as a director of the audition episodes, while Louis J. Horvitz replaced Gregg Gelfand as a director of the show.
Document 6: Rainbow (Kesha album): Rainbow is the third studio album by American singer Kesha. It was released on August 11, 2017, by Kemosabe and RCA Records. On July 5, 2017, Kesha announced via her Instagram account that she was releasing a single, titled ``Praying ''. The song was released alongside its accompanying music video and the album's pre-order.
Document 7: Rainbow (Mariah Carey album): Rainbow is the seventh studio album by American singer and songwriter Mariah Carey. It was released on November 2, 1999, by Columbia Records. The album followed the same pattern as Carey's previous two albums, "Daydream" (1995) and "Butterfly" (1997), in which she began her transition into the urban market. "Rainbow" contains a mix of hip hop-influenced R&B jams, as well as a variety of slow ballads. On the album, Carey worked with David Foster and Diane Warren, who, as well as Jimmy Jam & Terry Lewis, replaced Walter Afanasieff, the main balladeer Carey worked with throughout the 90s. As a result of her separation from her husband, Tommy Mottola, Carey had more control over the musical style of this album, so she collaborated with several artists such as Jay-Z, Usher, and Snoop Dogg, as well as Missy Elliott, Joe, Da Brat, Master P, 98°, and Mystikal.
Document 8: Music Box (Mariah Carey album): Music Box is the third studio album by American singer Mariah Carey. It was released by Columbia Records on August 31, 1993, in North America. The album comprises ballads primarily co-written by Carey and Walter Afanasieff, with whom she had previously worked on "Emotions" (1991), and a few urban dance tracks. During the course of the album's development, Carey wanted to broaden her audience, choosing a more pop/R&B oriented sound. During this time frame, she experimented with different musical instruments, leading the album's sound away from her more contemporary previous two efforts. Two unused tracks from the album sessions were released as B-sides: "Do You Think of Me" and "Everything Fades Away".
Document 9: American Idol: The top 12 finalists originally included Mario Vazquez, but he dropped out citing 'personal reasons' and was replaced by Nikko Smith. Later, an employee of Freemantle Media, which produces the show, sued the company for wrongful termination, claiming that he was dismissed after complaining about lewd behavior by Vazquez toward him during the show.
Document 10: Emotions (Mariah Carey album): Emotions is the second studio album by American singer and songwriter Mariah Carey. It was released on September 17, 1991 by Columbia Records. The album deviated from the formula of Carey's 1990 self-titled debut album, as she had more creative control over the material she produced and recorded. Additionally, "Emotions" features influences from a range of genres such as gospel, R&B, soul and 1950s, 1960s and 1970s balladry infusion. On the record, Carey worked with a variety of producers and writers, including Walter Afanasieff, the only hold over from her previous effort. Additionally, Carey wrote and produced the album's material with Robert Clivillés and David Cole from C+C Music Factory and Carole King, with whom she wrote one song.
Document 11: Someday (Mariah Carey song): "Someday" is a song by American singer and songwriter Mariah Carey from her self-titled debut studio album (1990). It is a dance-pop song with new jack swing influences. Prior to Carey signing a record contract, she and producer Ben Margulies had written and produced a four-track demo which included "Someday". After signing a contract with Columbia Records, Carey began work on her debut album and she reached out to Ric Wake to ask if he would produce the song, to which he agreed. The composition of the demo recording was changed during the recording process, most notably replacing the horns with a guitar, which Carey disapproved of.
Document 12: American Idol: In season eight, Latin Grammy Award-nominated singer–songwriter and record producer Kara DioGuardi was added as a fourth judge. She stayed for two seasons and left the show before season ten. Paula Abdul left the show before season nine after failing to agree terms with the show producers. Emmy Award-winning talk show host Ellen DeGeneres replaced Paula Abdul for that season, but left after just one season. On January 11, 2010, Simon Cowell announced that he was leaving the show to pursue introducing the American version of his show The X Factor to the USA for 2011. Jennifer Lopez and Steven Tyler joined the judging panel in season ten, but both left after two seasons. They were replaced by three new judges, Mariah Carey, Nicki Minaj and Keith Urban, who joined Randy Jackson in season 12. However both Carey and Minaj left after one season, and Randy Jackson also announced that he would depart the show after twelve seasons as a judge but would return as a mentor. Urban is the only judge from season 12 to return in season 13. He was joined by previous judge Jennifer Lopez and former mentor Harry Connick, Jr.. Lopez, Urban and Connick, Jr. all returned as judges for the show's fourteenth and fifteenth seasons.
Document 13: American Idol: American Idol employs a panel of judges who critique the contestants' performances. The original judges were record producer and music manager Randy Jackson, pop singer and choreographer Paula Abdul and music executive and manager Simon Cowell. The judging panel for the most recent season consisted of country singer Keith Urban, singer and actress Jennifer Lopez, and jazz singer Harry Connick, Jr. The show was originally hosted by radio personality Ryan Seacrest and comedian Brian Dunkleman, with Seacrest continuing on for the rest of the seasons.
Document 14: Charmbracelet: Charmbracelet is the ninth studio album by American singer and songwriter Mariah Carey, released on December 3, 2002 through MonarC Entertainment and Island Records. The album was her first release since her breakdown following the release of her film "Glitter" (2001) and its accompanying soundtrack album, both of which were critical and commercial failures from the previous year. Critics described "Charmbracelet" as one of her most personal records, following 1997's "Butterfly". Throughout the project, Carey collaborated with several musicians, including Jermaine Dupri, Jimmy Jam and Terry Lewis, 7 Aurelius and Dre & Vidal.
Document 15: Can't Take That Away (Mariah's Theme): "Can't Take That Away (Mariah's Theme)" is a song by American singer and songwriter Mariah Carey. It was released by Columbia Records on June 6, 2000, written by Carey and Diane Warren, and produced by Carey and Jimmy Jam and Terry Lewis for Carey's seventh studio album "Rainbow" (1999). It was released as the album's third single and a double A-side with "Crybaby". The song is a ballad, blending pop and R&B beats while incorporating its sound from several instruments including the violin, piano and organ. Lyrically, the song speaks of inner strength, and not allowing others to tear away your dreams.
ground_truth: one
sub_queries: Rainbow >> producer Answer: Mariah Carey
How many seasons was Mariah Carey a judge on American Idol? Answer: one