Given an integer `n`, return _a binary string representing its representation in base_ `-2`.

**Note** that the returned string should not have leading zeros unless the string is `"0"`.

**Example 1:**

    Input: n = 2
    Output: "110"
    Explantion: (-2)2 + (-2)1 = 2
    

**Example 2:**

    Input: n = 3
    Output: "111"
    Explantion: (-2)2 + (-2)1 + (-2)0 = 3
    

**Example 3:**

    Input: n = 4
    Output: "100"
    Explantion: (-2)2 = 4
    

**Constraints:**

*   `0 <= n <= 109`