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Later, though, the cops had a change of heart and told him he could pick up all the trash he wanted — though after last week’s scene when a man lit himself on fire, Mr. Cox said, he was told not to bring the gas can for his lawn mower.

“My message is to encourage Americans to stand shoulder to shoulder with the U.S. Park Service. They need to go to the park, go to the memorials, but go armed with a trash bag and a rake,” he said. “Ultimately, we are the stewards of our memorials at the end of the day.”

Jacqueline Klimas and Nathan Porter contributed to this report.