More like internationally. Cross country makes it sound like it's within the same country, to be honest, since it refers to crossing 'open country'. Look up 'cross country running', for instance.
In any case... I was so glad I was right about Kosaki. She was worried about Chitoge. And she finally figured out
why she would have left. She won't be able to let this go. She's going to want to talk to Chitoge. And so will Raku. That's why they're there, right?
Also, love her face at the end. What a shock!