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SAN DIEGO — Police shot and killed a man early Tuesday after a shootout and pursuit led to an 11-hour standoff at San Diego High School.

San Diego police said in an 11:30 a.m. update that two SWAT officers shot and killed 36-year-old Christopher Marquez as he hid inside a dumpster with a woman, who officers thought he was about to hurt.

Officers from National City first encountered Marquez around 8:15 p.m. Monday, when they tried to stop a car they believed he was inside. The driver sped off and a police chase ensued from I-805 and 43rd Street to the Loma Portal area.

Police said the car left the freeway briefly and when it re-entered, someone inside the car shot at a police vehicle near Nimitz and West Point Loma Boulevard. Officers continued to chase the driver into downtown, where police say someone in the car opened fire on officers again.

A third round of shots was fired at officers when the car stopped at San Diego High School, according to the San Diego Police Department. A National City officer shot back as two people ran off, one of them reportedly armed with a handgun and rifle.

Officers say Marquez holed himself up in a dumpster with a woman on school campus. A SWAT team and negotiators worked to get the pair to surrender for 11 hours. At one point, the woman surrendered a gun in exchange for water.

Police said Marquez got increasingly agitated and “apparently turned his anger toward the woman with him.” Officers said she tried to escape several times but Marquez pulled her back into the dumpster.

The police department said officers shot and killed Marquez when they saw him “maneuvering a rifle” toward the woman. The SWAT officers were in an elevated position, which allowed them to see inside the dumpster. Marquez was pronounced dead at the scene.

Marquez was wanted for allegedly shooting a bounty hunter, then opening fire on National City police officers weeks later. Police said the woman inside the dumpster with him was unhurt. They haven’t identified her and said they don’t know yet if she’ll face charges.

The names of the National City police officer who fired during the initial pursuit and the two San Diego Police SWAT officers who shot Marquez in the standoff are being withheld for now, the police department said.

Classes at San Diego High, East Village Middle College High School and Garfield High School were moved online because of the standoff.

Check back for updates on this developing story.