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The police, who have yet to make any arrests, said the assaults had been carried out by several hundred young men, whom they described as having a “North African or Arabic” appearance.

The nature and scale of the assaults have shocked Germany and brought to the surface social tensions over the willingness of Chancellor Angela Merkel’s government to throw open the doors to more than 1 million refugees last year.

Reker, who was elected last year, had already become a symbol of that embrace after being stabbed at a campaign event by a man angered over her welcoming attitude toward refugees. Her remarks have now made her a target of derision on all sides of the political spectrum.

Hundreds of women and men took to social media, posting angry responses and memes — including dozens showing the outstretched right arm known as the “Hitler Greeting” — under the hashtag #einearmlaenge, German for “an arm’s length.”

Even the country’s justice minister pushed back against the statement. “I don’t think much of tips for behaviour for women, such as ‘an arm’s length,'” Heiko Maas wrote on Twitter. “Not women are responsible, but the perpetrators.”

The police have so far been unable to apprehend anyone, a fact that Wolfgang Albers, Cologne’s chief of police, attributed to the chaos in which the assaults took place, despite there being dozens of officers on duty in the area.

“The women were in a very difficult situation,” Albers said in an interview Wednesday with public radio WDR 5. “They were afraid, they wanted to get away, and of course they did not notice any specific faces.”