All Distinct Card Hands

Medium

You hold cards with numbers cards, and some numbers may repeat. A hand is any selection of these cards, including none of them or all of them. Two hands that differ only in card order, or in which of several equal cards was picked, count as the same hand. Return all distinct hands. Each hand is a list of numbers; neither the order of the hands nor the order of numbers inside a hand matters.

Example 1

cards=[3, 1, 3] → [[1, 3, 3], [1, 3], [1], [3, 3], [3], []]

The two 3s look the same, so the hand [1, 3] appears only once. There are six hands: [], [1], [3], [1, 3], [3, 3], [1, 3, 3].

Example 2

cards=[-2, -2] → [[-2, -2], [-2], []]

You can take nothing, one -2, or both.

Constraints

1 ≤ len(cards) ≤ 10
-10 ≤ cards[i] ≤ 10

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Topics

Bit Manipulation Array Backtracking

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Input

cards=[3, 1, 3]

Expected

[[1, 3, 3], [1, 3], [1], [3, 3], [3], []]

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