Inspired by Problem 42831, this problem aims to calculate the integer complexity for large numbers. The integer complexity of a natural number n is defined as the least number of 1’s required to express n using only the two operations + and × and parentheses.

Example: the number 11 may be represented using 8 ones:

    11 = (1 + 1 + 1) × (1 + 1 + 1) + 1 + 1.

However, it has no representation using 7 or fewer ones. Therefore, its complexity is 8.

Your solution will be scored based on its running time. No cheating please.

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Last Solution submitted on Dec 02, 2025

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George Berken Mehdi Dehghan DH 煊

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