Background: Green Day is an American punk rock band formed in 1986 by lead vocalist and guitarist Billie Joe Armstrong and bassist Mike Dirnt. For much of the band's career, they have been a trio with drummer Tre Cool, who replaced John Kiffmeyer in 1990 prior to the recording of the band's second studio album, Kerplunk (1991). Guitarist Jason White, who has been a touring member since 1999, was an official member from 2012 to 2016. Green Day was originally part of the punk scene at the DIY 924 Gilman Street club in Berkeley, California.
Context: Kerplunk's underground success led to a number of major record labels being interested in signing Green Day, and the band eventually left Lookout! and signed to Reprise Records after attracting the attention of producer Rob Cavallo. The group was impressed by his work with fellow Californian band The Muffs, and later remarked that Cavallo "was the only person we could really talk to and connect with". Reflecting on the period, Armstrong told Spin magazine in 1999, "I couldn't go back to the punk scene, whether we were the biggest success in the world or the biggest failure ... The only thing I could do was get on my bike and go forward." After signing with Reprise, the band went to work on recording its major label debut, Dookie. Recorded in three weeks, and released in February 1994, Dookie became a commercial success, helped by extensive MTV airplay for the videos of the songs "Longview", "Basket Case", and "When I Come Around", all of which reached the number one position on the Modern Rock Tracks charts. The album went on to sell over 10 million copies in the US. At a performance on September 9, 1994 at Hatch Memorial Shell in Boston, mayhem broke out during the band's set (cut short to seven songs) and by the end of the rampage, 100 people were injured and 45 arrested. The band also joined the lineups of both the Lollapalooza festival and Woodstock '94, where the group started an infamous mud fight. During the concert, a security guard mistook bassist Mike Dirnt for a stage-invading fan and punched out some of his teeth. Viewed by millions by pay-per-view television, the Woodstock 1994 performance further aided Green Day's growing publicity and recognition, and helped push its album to eventual diamond status. In 1995, Dookie won the Grammy Award for Best Alternative Album and the band was nominated for nine MTV Video Music Awards including Video of the Year. In 1995, a new single for the Angus soundtrack was released, entitled "J.A.R.". The single debuted at number one on the Billboard Modern Rock Tracks chart. The song was followed by the band's fourth studio album, Insomniac, which was released in the fall of 1995. Insomniac was a much darker and heavier response to the band's newfound popularity, compared to the more melodic Dookie. The album opened to a warm critical reception, earning 4 out of 5 stars from Rolling Stone, which said "In punk, the good stuff actually unfolds and gains meaning as you listen without sacrificing any of its electric, haywire immediacy. And Green Day are as good as this stuff gets." The singles released from Insomniac were "Geek Stink Breath", "Stuck with Me", "Brain Stew/Jaded", and "Walking Contradiction". Though the album did not approach the success of Dookie, it sold two million copies in the United States. In addition, the album won the band award nominations for Favorite Artist, Favorite Hard Rock Artist, and Favorite Alternative Artist at the 1996 American Music Awards, and the video for "Walking Contradiction" got the band a Grammy nomination for Best Video, Short Form, in addition to a Best Special Effects nomination at the MTV Video Music Awards. After that, the band abruptly cancelled a European tour, citing exhaustion. CANNOTANSWER
Question: Did they win a grammy?. Whats the answer?

won the Grammy Award for Best Alternative Album