Numbers That Survive a Flip

Medium

Turn a sign with a number on it by 180° and the digits 0, 1 and 8 stay the same, 6 becomes 9 and 9 becomes 6. Every other digit stops being a digit at all. Call a number *flip-proof* if it reads exactly the same after that turn. For example, 69 and 818 are flip-proof, while 16 is not. Return every flip-proof number of length length as a string. Numbers have no leading zeros: the first digit cannot be 0 unless the number is a single digit. The order of the answer doesn't matter.

Example 1

length=1 → ['0', '1', '8']

Among single digits only 0, 1 and 8 stay themselves after the turn.

Example 2

length=3 → ['101', '808', '609', '906', '111', '818', '619', '916', '181', '888', '689', '986']

The outer digits are one of the pairs 1…1, 8…8, 6…9, 9…6, and the middle is 0, 1 or 8: 4 · 3 = 12 numbers.

Constraints

1 ≤ length ≤ 14

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Topics

Recursion Array String

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Input

length=1

Expected

['0', '1', '8']

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