Sum of Intervals

Write a function called sumIntervals/sum_intervals that accepts an array of intervals, and returns the sum of all the interval lengths. Overlapping intervals should only be counted once.

Intervals

Intervals are represented by a pair of integers in the form of an array. The first value of the interval will always be less than the second value. Interval example: [1, 5] is an interval from 1 to 5. The length of this interval is 4.

Overlapping Intervals

List containing overlapping intervals:

[
   [1, 4],
   [7, 10],
   [3, 5]
]

The sum of the lengths of these intervals is 7. Since [1, 4] and [3, 5] overlap, we can treat the interval as [1, 5], which has a length of 4.

Examples:

sumIntervals( [
   [1, 2],
   [6, 10],
   [11, 15]
] ) => 9

sumIntervals( [
   [1, 4],
   [7, 10],
   [3, 5]
] ) => 7

sumIntervals( [
   [1, 5],
   [10, 20],
   [1, 6],
   [16, 19],
   [5, 11]
] ) => 19

sumIntervals( [
   [0, 20],
   [-100000000, 10],
   [30, 40]
] ) => 100000030

Tests with large intervals

Your algorithm should be able to handle large intervals. All tested intervals are subsets of the range [-1000000000, 1000000000].

### Encodings

purity: `LetRec`  
numEncoding: `ScottBinary` ( subsets are actually in range `[0, 2000]` )  
export constructor `Pair` for your `Pair` encoding  
export constructors `nil, cons` for your `List` encoding