At least 677,000 Ukrainians have fled their country as of Tuesday, the sixth day of Russia’s invasion, according to UNHCR, the U.N. refugee agency.

It’s an exodus that shows no signs of slowing, and appears set to become the largest refugee crisis in Europe this century, UNHCR says. 

At Ukraine’s border with Poland, refugees line up for more than 20 miles in freezing temperatures, yearning for safety, Chris Livesay reports for “CBS Mornings.”

At Lviv’s main train station in western Ukraine, thousands more try desperately to get out. 

But not everyone can. Women and small children are fleeing the country while men of fighting age are running into battle.

Men, some difficult not to call boys, now face frontline combat, even though they’ve never held a gun, like 18-year-old medical student Jaroslav.

He said he never imagined facing something like this: “It’s like a nightmare.”  

Half of those who have fled are in Poland. Some 90,000 are in Hungary. And 60,000 are in Moldova, 50,000 are in Slovakia and 40,000 are in Romania, Filippo Grandi, the U.N. High Commissioner for Refugees, said Tuesday.

“People are on the move, and more will come,” he said.

Pamela Falk contributed to this report.