Even Piles of Cards

Easy

Every card in a deck has a number on it, and the deck is given as the array cards. Split the whole deck into piles so that: - every pile holds the same number of cards k, with k ≥ 2; - all cards within a pile show the same number. Every card must go into exactly one pile. Return True if such a split exists, and False otherwise.

Example 1

cards=[5, 2, 5, 2, 2, 5, 2, 5, 5, 5] → True

There are six 5s and four 2s. Both counts divide by 2, giving five piles of 2 cards.

Example 2

cards=[7, 7, 7, 1, 1] → False

There are three 7s and two 1s. No number greater than 1 divides both 3 and 2, so it cannot be done.

Example 3

cards=[4] → False

Constraints

1 ≤ len(cards) ≤ 10⁴
0 ≤ cards[i] < 10⁴

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Topics

Array Hash Table Math Counting Number Theory

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Input

cards=[5, 2, 5, 2, 2, 5, 2, 5, 5, 5]

Expected

True

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