Get an array of classes inheritances

I am trying to generate a multidimensional array of the inheritances tree from a given list of classes.

Input ['A', 'B', 'C', 'D']

class A {}

class B extends A {}

class C extends A {}

class D extends C {}

The desired output would be something like this

[
  'A' => false,
  'B' => [
    'A' => false
  ],
  'C' => [
    'A' => false
  ],
  'D' => [
    'C' => [
      'A' => false
    ]
  ]
]

I could not go any further then this without a headache.

function getTree(array $classes) {
  $paths = [];

  foreach($classes as $class) {
    if (! class_exists($class))
      continue;

    $class = new ReflectionClass($class);

    if (! isset($paths[$class->getName()]))
      $paths[$class->getName()] = false;

    while($parent = $class->getParentClass()) {
      $paths[$class->getName()] = $parent->getName();
      $class = $parent;
    }
  }

  return $paths;
}

$tree = getTree(['A', 'B', 'C', 'D']);

print_r($tree);

Array
(
    [A] => 
    [B] => A
    [C] => A
    [D] => C
)

Anyone got a hint to help me accomplish this?

Thank you