Welcome to the Ice Barn

Ice Barn is a rather rare Nikoli type. Rules go something like:

Draw a directed path from IN to OUT, visiting all the ice barns (grey areas) along the way. You move from cell centre to adjacent cell centre in an orthogonal fashion. You may not backtrack, overlap or branch. You may not turn inside a barn. Crossing your path is only allowed inside barns. In some puzzles, parts of the path will be given; an arrowhead on them indicates direction of movement along them.

I've got some nerve publishing this: I wrote this a couple of hours after learning this puzzle type existed. The solution is more symmetric than the grid, so I think that's obvious.

I have to say I love the Japanese naming connotations. Ice, because of the sliding inside presumably. And barn, because, um... , that's where you usually revisit your past actions? Or keep your ice, for that matter.