Question: In between John Woo and Alejandro González Iñárritu who is the first Mexican director to be nominated for the Academy Award for Best Director for "Babel" (2006)?

Context paragraphs:
Benicio del Toro: Benicio Monserrate Rafael del Toro Sánchez (born February 19, 1967) is a Puerto Rican actor.  He won an Academy Award, BAFTA Award, Golden Globe Award and Screen Actors Guild Award for his portrayal of the jaded but morally upright police officer Javier Rodriguez in the film "Traffic" (2000).  Del Toro's performance as ex-con turned religious fanatic in despair, Jack Jordan, in Alejandro González Iñárritu's "21 Grams" (2003) earned him a second Academy Award nomination for Best Supporting Actor, as well as a second Screen Actors Guild Awards nomination and a BAFTA Awards nomination for Best Actor in a Leading Role.

21 Grams: 21 Grams is a 2003 American drama film directed by Mexican director Alejandro González Iñárritu from a screenplay written by Guillermo Arriaga.  It stars Sean Penn, Naomi Watts, Charlotte Gainsbourg, Danny Huston and Benicio Del Toro.

Ryo Sugimoto: Ryo Sugimoto Born in 1976.  Sugimoto worked on number of films as an art assistant under Production Designer Mitsuo Harada and Yohei Taneda.  Sugimoto joined NOUVELLE VAGUE Co.,Ltd .  in 2005, has worked on films such as "AEGIS"and "Tokyo Tower" as a set designer and was the art director on "BABEL"(Dir: Alejandro González Iñárritu) which won the Art Excellence in Production Design Award(2006) from the Art Directors Guild.  Sugimoto was the first Production Designer for Junji Sakamoto "Chameleon"(2007), and is the Production designer for "Map of the sounds of Tokyo" directed by Isabel Coixet.  Sugimoto also provides designs for commercials, music videos and interiors,

Babel (film): Babel is a 2006 drama film directed by Alejandro González Iñárritu and written by Guillermo Arriaga, starring an ensemble cast.  The multi-narrative drama completes Iñárritu's "Death Trilogy", following "Amores perros" and "21 Grams".  It is an international co-production among companies based in the United States and Mexico.  The film portrays multiple stories taking place in Morocco, Japan, Mexico and the US.

Amores perros: Amores perros is a 2000 Mexican drama thriller film directed by Alejandro González Iñárritu and written by Guillermo Arriaga.  "Amores perros" is the first installment in González Iñárritu's "Trilogy of Death", succeeded by "21 Grams" and "Babel".  It is an anthology film constructed as a triptych: it contains three distinct stories connected by a car accident in Mexico City.  The stories centre on a teenager in the slums who gets involved in dogfighting; a model who seriously injures her leg; and a mysterious hitman.  The stories are linked in various ways, including the presence of dogs in each of them.

John Woo: John Woo SBS (Ng Yu-Sum; born 1 May 1946) is a Chinese-born Hong Kong film director, writer, and producer.  He is the owner of Lion Rock Productions.  He is considered a major influence on the action genre, known for his highly chaotic action sequences, Mexican standoffs, and frequent use of slow motion.  Woo has directed several notable Hong Kong action films, among them, "A Better Tomorrow" (1986), "The Killer" (1989), "Hard Boiled" (1992), and "Red Cliff" (2008/2009).

Michael Punke: Michael W. Punke (born December 7, 1964) is an American writer, novelist, professor, policy analyst, policy consultant, attorney, and former Deputy United States Trade Representative and US Ambassador to the World Trade Organization in Geneva, Switzerland.  He is currently the Vice President of Public Policy for Amazon Web Services.  He is best known for writing "The Revenant: A Novel of Revenge" (2002), which was adapted into film as "The Revenant" (2015), directed by Alejandro González Iñárritu, with a screenplay by Iñárritu and Mark L. Smith, and starring Leonardo DiCaprio and Tom Hardy.

Biutiful: Biutiful is a 2010 Mexican-Spanish drama film directed by Alejandro González Iñárritu and starring Javier Bardem.  It is González Iñárritu's first feature since "Babel" and fourth overall, and his first film in his native Spanish language since his debut feature "Amores perros".  The title "Biutiful" refers to the phonological spelling in Spanish of the English word "beautiful".

Aoife McArdle: Aoife McArdle is an Irish writer and director.  Her work includes music videos for Jon Hopkins and U2 as well as television commercials for Honda, Samsung and Under Armour (with Bryce Harper and Cam Newton).  Her video for the U2 song 'Every Breaking Wave' was nominated for Best International Music Video at the UK Music Video Awards 2015 and was publicly praised by Academy award winning directors Terry George, Alejandro González Iñárritu and Spike Jonze.  She was nominated for Best Director at the UK Music Video Awards in 2014 and nominated for Best Director at the Ciclope Festival 2016 .  Her first feature-length film, 'Kissing Candice', premiered at the Toronto International Film Festival on 8th September 2017.

Alejandro González Iñárritu: Alejandro González Iñárritu (] ; credited since 2014 as Alejandro G. Iñárritu; born August 15, 1963) is a Mexican film director, producer, and screenwriter.  He is the first Mexican director to be nominated for the Academy Award for Best Director and the Directors Guild of America Award for Outstanding Directing for "Babel" (2006).

Supporting paragraphs: John Woo Alejandro González Iñárritu
Answer: Alejandro González Iñárritu