Best Order of Binary Pieces

Medium

You are given three positive integers pieces. Write each one in binary (no leading zeros) and join the three strings in some order. The result is the binary form of a new number. Return the largest number you can build this way.

Example 1

pieces=[2, 5, 1] → 54

In binary these are "10", "101" and "1". The order 1, 5, 2 gives "110110" = 54, more than any other order.

Example 2

pieces=[4, 4, 3] → 228

"11" has to go first: "11100100" = 228.

Example 3

pieces=[1, 1, 1] → 7

Constraints

len(pieces) = 3
1 ≤ pieces[i] ≤ 127

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Topics

Bit Manipulation Array Enumeration

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Input

pieces=[2, 5, 1]

Expected

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