How to convert php hierarchical array in nested sets?

I have a hierarchical array.

Array
(
    [0] => Array
        (
            [id] => 28
        )

    [1] => Array
        (
            [id] => 29
        )

    [2] => Array
        (
            [id] => 30
            [children] => Array
                (
                    [0] => Array
                        (
                            [id] => 31
                        )

                )

        )

)
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I need to get keys «left», «right» and «depth» for nested sets.

I found a similar question here: php convert array into a hierarchical nested set for database.

But answer from this branch doesn’t work correctly.

It doesn’t have key «depth» and calculation of keys «left» and «right» is not correct.

Expected Result:

Array
(
    [0] => Array
        (
            [id] => 27
            [lft] => 1
            [rgt] => 10
            [depth] => 0
        )

    [1] => Array
        (
            [id] => 28
            [lft] => 2
            [rgt] => 3
            [depth] => 1
        )

    [2] => Array
        (
            [id] => 29
            [lft] => 4
            [rgt] => 5
            [depth] => 1
        )

    [3] => Array
        (
            [id] => 30
            [lft] => 6
            [rgt] => 9
            [depth] => 1
        )

    [4] => Array
        (
            [id] => 31
            [lft] => 7
            [rgt] => 8
            [depth] => 2
        )
)
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[id] => 27 - : this is a root node, but I do not show it to users.

Please help me to solve this problem.