It was about 2 a.m. on a moonless October night in 1987 when the police chief of a small northern Vermont town spotted a man carrying a black bag and walking down the railroad tracks from Canada toward a waiting van about a mile south of the border.

The man turned out to be linked to a Lebanese extremist group. And in his bag, later recovered from a ditch, were a ski mask and a propane-canister bomb.

“If it had been two minutes later, they would have been in the van and gone on their way, and I’d have never known the difference,” recalled Richford’s long-retired police chief, Richard Jewett, who won numerous awards for apparently foiling an attack. “I guess luck was on my side.”

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Whether it was luck or not, Jewett beat the odds in a way. While U.S. President Donald Trump, in arguing for a border wall, has said repeatedly that terrorists are slipping across from Mexico, known cases of extremists entering the U.S. through its land borders to the north or the south are exceedingly rare.

Even then, State Department reports on terrorism have expressed more concern about the Canadian border than the Mexican one because Canada, unlike Mexico, has been home to “violent extremists inspired by terrorist groups such as ISIS and al-Qaida and their affiliates and adherents,” according to a 2017 paper.

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A study issued last month by the libertarian Cato Institute found that between 1975 and 2017, seven people from “special interest” countries – states tied at least loosely to terrorism – were convicted of planning attacks on U.S. soil. Four of those individuals entered illegally from Canada, none from Mexico.

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The only known terrorists who crossed illegally from Mexico in the 42-year span covered by the Cato study were three ethnic Albanians from Macedonia who came as children with their parents in 1984 and, in their 20s, were arrested in a foiled plot to attack the Army’s Fort Dix in New Jersey, in 2007.

“This shows how rare it is for people to try to enter the U.S. illegally as terrorists by crossing a border,” said Alex Nowrasteh, one of the authors of the Cato study. “It shows how Mexico is not how these folks typically try to enter and the terrorism justification for building the wall is probably the weakest.”

In fact, most people with terroristic intent come into the country by air and are typically in the United States legally. The 19 men who carried out the 9-11 attacks all entered the country legally. The brothers who carried out the 2013 Boston Marathon bombing that killed three people entered the U.S. on tourist visas with their families and were later granted asylum.

On the Canadian border, Ahmed Ressam was caught by border agents in December 1999 after he tried to enter the United States at Port Angeles, Washington, with bomb components in the trunk of his car. It was later determined Ressam planned to attack the Los Angeles airport during the millennium.

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“The evidence shows that if we are going to talk about terrorism, there is actually good reason to think more carefully about the U.S.’s northern border than the U.S.’s southern border,” said Emily Gilbert, a terrorism expert and director of the Canadian studies program at the University of Toronto.

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The U.S.-Canadian border is over 5,500 miles (8,900 kilometres) long, more than 2 1/2 times the length of the U.S. border with Mexico, and is crossed by numerous roads and railroad tracks, with many wide-open stretches. In Richford, the border cuts through farm fields and forests with occasional granite markers in the ground.

Worries about terrorists crossing from Canada have been reduced by the close co-operation between the two countries, and security has been tightened since 9-11. Hundreds more Border Patrol agents are stationed along the border (authorities won’t disclose the total), surveillance has been enhanced with such things as electronic sensors and helicopters, and those trying to cross the border must show a passport or certain other documents, none of which were required before Sept. 11, 2001.

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In the Richford incident, Walid Kabbani was seized at the border, and his two accomplices in the van were arrested at a local hotel the morning after. U.S. authorities said the three men, Lebanese-born Canadians from Montreal, were members of an extremist group responsible for the 1982 assassination of Lebanese President-elect Bashir Gemayel.

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Federal officials were never able to say for sure what their intended target was. All three were convicted or pleaded guilty to explosives and immigration violations and went to prison, getting out in the 1990s.

Terrorism was the last thing on Jewett’s mind when he became police chief in the border town, which has around 2,300 people and is about 2,000 miles from the Mexican border. He said the current debate about a border wall with Mexico and the recent 35-day government shutdown it provoked has gone too far.

“I do also understand we need some protections on our borders. And I just don’t know what it is,” Jewett said. “It’s hard.”

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AP researcher Rhonda Shafner in New York contributed to this report