John Woo
John Woo Yu-Sen SBS (; born 1 May 1946) is a Hong Kong film director, producer and screenwriter. He is considered a major influence on the action genre, known for his highly chaotic action sequences, stylized imagery, Mexican standoffs, frequent use of slow motion and allusions to neo-noir, "wuxia" and Western cinema. He was also a pioneer of "heroic bloodshed" films (a crime action film genre involving Chinese triads) and the "gun fu" genre in Hong Kong action cinema, before working in Hollywood films.
John Woo
Considered one of the major figures of Hong Kong cinema, Woo has directed several notable action films in his adopted home, among them, "A Better Tomorrow" (1986), "The Killer" (1989), "Hard Boiled" (1992), and "Red Cliff" (2008/2009). He is a winner of the Hong Kong Film Awards for Best Director, Best Editing, and Best Picture, as well as a Golden Horse Award, an Asia Pacific Screen Award, and a Saturn Award.
Alejandro González Iñárritu
Alejandro González Iñárritu ( ; ] ; born 15 August 1963) is a Mexican film director, producer, and screenwriter. He is known for telling international stories about the human condition, and his projects have garnered critical acclaim and numerous accolades.
Alejandro González Iñárritu
His debut film, "Amores Perros", premiered at the Cannes Film Festival and won the Critics' Week Grand Prize and was nominated for an Academy Award for Best Foreign Language Film in 2000. His next and first American film, "21 Grams", was presented in competition at the 60th Venice International Film Festival, where Sean Penn won the Volpi Cup for Best Actor. It was nominated for two Academy Awards for Lead Actress Naomi Watts and Supporting Actor Benicio del Toro. In 2006, "Babel" was presented in competition at the 59th Cannes Film Festival where Iñárritu won the Best Director Award. That same year, "Babel" went on to win the Golden Globe Award for Best Picture Drama, was nominated for the Directors Guild of America Award for Outstanding Directing, and was nominated for seven Academy Awards, including two for Iñárritu for Best Picture and Best Director. Iñárritu's fourth film, "Biutiful", received the Best Actor Award at the Cannes Film Festival for Javier Bardem's moving lead performance. Additionally, the film was nominated for an Academy Award for Best Foreign Language Film, and Javier Bardem was nominated for an Academy Award for Best Actor. In 2014, he won three Academy Awards: Best Picture, Best Director, and Best Original Screenplay for "Birdman or (The Unexpected Virtue of Ignorance)". The following year, he won a second Academy Award for Best Director for "The Revenant" (2015), making him the third director to win back-to-back Academy Awards, and the first since 1950. "The Revenant" also won Iñárritu a DGA Award, making history as the first person to ever win two in a row. Additionally, Iñárritu was awarded a Special Achievement Academy Award for his virtual reality installation "Carne y Arena" in 2017, the first time it had been awarded since 1995. Carne y Arena also became the first VR installation ever presented at the Cannes Film Festival in 2017 and it was exhibited at Fondazione Prada in Milan, LACMA in Los Angeles, Tlatelolco in Mexico City and in Washington DC at a converted church in the northeast sector of the city.

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)?
Answer: Alejandro González Iñárritu