Officer Rob Addea positioned himself directly beneath the narrow, rain-slicked ledge and pleaded with the “paranoid” woman above.

“Just get the kids back inside!” he implored. “Please. Please. That’s all we want you to do.”

It was 4 p.m. Saturday, and police in Delray Beach, Fla., had apparently just stumbled into someone’s madness.

A 23-year-old mother, who police said was agitated, deranged and high on the narcotic “Molly,” was hallucinating and becoming increasingly unstable, as the worried neighbors who called 911 could clearly see.

Worst of all, she had brought her 1-year-old son and 3-year-old daughter onto the slippery ledge with her, and the toddlers were terrified.

“It appeared that the children would either fall or be pushed off the roof by [the woman] herself … which would have caused certain serious injury and/or death to them both,” a police report said.

Officers scrambled to the scene, improvising a plan to rescue the children and subdue their mother — their moves captured by body cameras in footage that was ultimately uploaded to the department’s Facebook page.

Addea, a 14-year veteran of the department with two small children of his own, was the first on the scene. He patrols the southeastern part of Delray Beach and told The Washington Post that he has had about 40 hours of training on how to respond to people in mental crises. “I feel like I can talk to anybody,” he said Thursday. “I have a reputation as being someone who can de-escalate things.”

But this situation was dire.

It was raining. One child was wearing just leggings; another only a diaper. The only thing that separated them from a potentially deadly fall was a few inches of an overhang and a flimsy rain gutter. Their mother “was very fragile emotionally,” police said, and appeared to be getting worse.

“You don’t have time to sit down and call timeout and make a plan with something like that,” Addea told The Post. “This is a poker game. She holds all the cards. Those kids, she could push them off or they could fall off at any second.”

If he burst into the house and dashed up the stairs, the sudden move could startle the woman into doing something rash, and he wouldn’t be there to catch a falling child.

As other officers sped to the scene, Addea knew what he had to do: “Let me just buy us time,” he told himself.

But how do you reason with a person who may be beyond reason?

The woman thought that the officers were lying to her about who they really were and that they would kill her and her children.

She thought someone had hacked into her phone. Escalating matters, the police were being subsumed into her hallucination: To her, the officer telling her everything would be okay was one of the evil agents who had come for her, Addea said.

He also worried about physics. The ledge was wet and slightly sloped. The children were barefoot.

“There’s genuine fear in those cries,” Addea said of the children. “Your reaction is always to help that person — to immediately go to the aid of a distressed child. I have two kids myself, a 5-year-old and 2-year old, and your brain automatically puts them up there. And suddenly you’re a worried father.”

He pushed those thoughts away as other officers arrived. “We needed a team effort to get to her,” he recalled.

He reassured the woman that she wasn’t in trouble, that he was there to help and that, yes, he was an actual police officer.

Other officers went for tools to break down the home’s front door, but one person standing outside gave them the door code.

A little later, they were inside the house, up the stairs and on the ledge. “It’s okay. It’s okay. Police. We’re here to help, okay,” one officer said.

It was, Addea believes, the most dangerous moment of the whole encounter: No one knew how the woman would react to the sudden presence of officers on the ledge. And the children were still vulnerable in her grasp.

The woman began screaming at Addea’s colleagues — Sgt. Brian Griffith and Sgt. Mike DeBree — repeating her claims that they weren’t real police officers.

She threw her cellphone to the ground.

Griffith flipped open his badge and held it out to the woman.

DeBree edged closer to the children.

Then, he clamped a hand around each of their arms.

The children screamed as they were gripped by a stranger. “Help me!” the girl shrieked. “I’m scared!”

It’s unclear whether she was more afraid of the height, her mother’s unstable moment or the things she had been warned about the officer.

Slowly, the children were led through a neighbor’s window.

Officers wrestled the flailing woman into handcuffs.

She had taken the narcotic “Molly,” the street name for MDMA, police later learned.

The drug exacerbated an unidentified preexisting mental condition, sparking the paranoia and hallucinations, police said.

The woman — whose identity was not released — was taken to a hospital for treatment and faces two charges of child abuse when she gets out. Her boyfriend, who authorities say provided the drug, also could be charged.

The Department of Children and Families took custody of the children.

On Thursday morning, days after the rescue, Addea said the entire time he was in the situation, he was trying to quell “a roller coaster of emotions” so no one ended up hurt.

“In this business, you hear about sad things happening all the time,” he said. “And you’re just like  — let’s not let this be one. Let’s do the right thing.”

He received his assurance a few minutes after the situation was defused, as he shifted from ending a crisis to writing a police report.

For a moment, he watched the children, who were now safe.

“They were very resilient and seemed to have been snapped back into ‘kid’ mode,” he said. “They were just kind of running around being kids. They were happy that we were there.”

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