Finding common complete path between multiple input nodes

But the same query works for the inputs "A","B", "H'.

WITH ["A", "B","H"] AS names
UNWIND names AS nn
MATCH (n {name: nn})
WITH collect(n) AS nds

UNWIND nds AS n1
UNWIND nds AS n2
WITH nds, n1, n2 WHERE id(n1) > id(n2)
MATCH path = allShortestPaths((n1)--(n2))
WITH nds, path WHERE ALL(n IN nds WHERE n IN nodes(path))
RETURN path ORDER BY length(path) ASC

Output:
image