Palindrome From Two Factors

Hard

Take two integers, each with exactly width digits (no leading zeros), and multiply them. Among all such products, find the largest one that is a palindrome, meaning it reads the same forwards and backwards. The number can be huge, so return it modulo 1337.

Example 1

width=2 → 987

The largest palindrome is 9009 = 99 · 91, and 9009 mod 1337 is 987.

Example 2

width=1 → 9

With one-digit factors the best palindrome is 9 = 1 · 9 (or 3 · 3).

Example 3

width=3 → 123

Constraints

1 ≤ width ≤ 8

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Topics

Math Enumeration

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Input

width=2

Expected

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