<p>You are given an array of non-overlapping intervals <code>intervals</code> where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> represent the start and the end of the <code>i<sup>th</sup></code> interval and <code>intervals</code> is sorted in ascending order by <code>start<sub>i</sub></code>. You are also given an interval <code>newInterval = [start, end]</code> that represents the start and end of another interval.</p>

<p>Insert <code>newInterval</code> into <code>intervals</code> such that <code>intervals</code> is still sorted in ascending order by <code>start<sub>i</sub></code> and <code>intervals</code> still does not have any overlapping intervals (merge overlapping intervals if necessary).</p>

<p>Return <code>intervals</code><em> after the insertion</em>.</p>

<p><strong>Note</strong> that you don&#39;t need to modify <code>intervals</code> in-place. You can make a new array and return it.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> intervals = [[1,3],[6,9]], newInterval = [2,5]
<strong>Output:</strong> [[1,5],[6,9]]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
<strong>Output:</strong> [[1,2],[3,10],[12,16]]
<strong>Explanation:</strong> Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= intervals.length &lt;= 10<sup>4</sup></code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>intervals</code> is sorted by <code>start<sub>i</sub></code> in <strong>ascending</strong> order.</li>
	<li><code>newInterval.length == 2</code></li>
	<li><code>0 &lt;= start &lt;= end &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def insert(self, intervals: List[List[int]], newInterval: List[int]) -> List[List[int]]:
        #  |-| |--|    |---|
        # |---| |---| |---|

        # Start and End can either be inside an interval or outside
        # Iterate over each and track index is inside for just after it
        # If start is inside, track index. Outside, track index before
        # If end is inside, track index. Outside, track index after
        new_start, new_end = newInterval

        start_in, end_in = None, None
        start_index, end_index = len(intervals), len(intervals)
        
        for i in range(len(intervals)):
            start, end = intervals[i]

            if start <= new_start and new_start <= end:
                start_in = True
                start_index = i
            elif start_in is None and new_start < start:
                start_in = False
                start_index = i

            if start <= new_end and new_end <= end:
                end_in = True
                end_index = i
            elif end_in is None and new_end < end:
                end_in = False
                end_index = i - 1

        print(start_in, start_index)
        print(end_in, end_index)

        # If start is in, place before and first of start_index. If out, place before and new_start
        # If end is in, place last of end_index and after. If out, place new_end and after

        new_list = []

        for i in range(start_index):
            new_list.append(intervals[i])

        middle_interval = [
            intervals[start_index][0] if start_in else new_start,
            intervals[end_index][1] if end_in else new_end
        ]

        new_list.append(middle_interval)

        for i in range(end_index + 1, len(intervals)):
            new_list.append(intervals[i])

        return new_list
        

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