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# Merge Intervals

Problem Description

Given a set of non-overlapping intervals and a new interval.

Insert the new interval into the set of intervals (merge if necessary).

You may assume that the intervals were initially sorted according to their start times.
Note: Make sure the returned intervals are also sorted.

Problem Constraints
0 <= |intervals| <= 106
1 <= intervalsi.start < intervalsi.end <= 109
1 <= newInterval.start < newInteval.end <= 109

Input Format
The First argument is an array of Intervals.
The second argument is the new Interval.

Output Format
Return the array of merged intervals.

Example Input
Input 1:
```Intervals = [[1,3],[6,9]]
newInterval = [2,5]```
Input 2:
```Intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]]
newInterval = [4,9]```

Example Output
Output 1:
`[[1,5],[6,9]]`
Output 2:
`[1,2],[3,10],[12,16]`

Example Explanation
Explanation 1:
`Given intervals [1,3],[6,9] insert and merge [2,5] would result in [1,5],[6,9].`
Explanation 2:
```Given [1,2],[3,5],[6,7],[8,10],[12,16], insert and merge [4,9] would result in [1,2],[3,10],[12,16].
This is because the new interval [4,9] overlaps with [3,5],[6,7],[8,10].```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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