Find POPUP — hide sibling nodes up the DOM tree

Find POPUP (DOM tree manipulation). Given a DOM tree of DomNodes, implement openPopup(): locate the node with id POPUP, hide all of POPUP's siblings, then find POPUP's parent and hide all of the parent's siblings. (Hiding means setting hidden = true; POPUP and its ancestors stay visible.)

// Initial:                          // After openPopup():
//        ROOT                       //        ROOT
//     /   |   \                     //     /   |   \
//    B    C    D                    //   (B)  (C)   D
//  / |      / | \ \                 //  / |      / | \  \
// F  G  POPUP I J K                 // F  G   POPUP (I)(J)(K)
//      / | \                        //       / | \
//     N  O  P                       //      N  O  P

class DomNode {
    String id;
    boolean hidden;
    List<DomNode> children;
}