Writing Numbers in Base Minus Two

Medium

In base -2 the only digits are 0 and 1, and digit number i (counting from the right, starting at zero) is worth (-2)^i: 1, -2, 4, -8, 16, and so on. For example, the string "110" means 4 − 2 = 2. Given a non-negative integer n, return its base -2 representation as a string without leading zeros. For n = 0 the answer is "0".

Example 1

n=6 → '11010'

(-2)⁴ + (-2)³ + (-2)¹ = 16 − 8 − 2 = 6, hence "11010".

Example 2

n=0 → '0'

Zero is written as the single digit "0".

Example 3

n=7 → '11011'

Constraints

0 ≤ n ≤ 10⁹

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Topics

Math

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Input

n=6

Expected

'11010'

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