Find safe travel intervals between planet influences

You are planning a space route along a one-dimensional line (the x-axis).

You are given a list of planets. Each planet is represented by an integer pair ((c, r)):

• c is the coordinate of the planet's center on the x-axis.
• r is a non-negative integer radius of its gravitational influence.

A point x on the x-axis is unsafe for a space traveler if it lies within the gravitational influence of at least one planet:

[ |x - c_i| \le r_i \quad \text{for some planet } i ]

Equivalently, each planet makes the interval ([c_i - r_i,; c_i + r_i]) unsafe.

Task:

• Consider the entire real line as the possible travel path.
• Compute all maximal continuous intervals on this line where the traveler is safe , i.e., points not covered by any planet's unsafe interval.
• Return these safe intervals as a sorted list of disjoint intervals.

Representation details:

• Represent each safe interval as a pair (start, end) with start < end .
• Intervals may be unbounded on the left or right:
  • Use -∞ for an interval unbounded to the left (e.g., (-∞, a) ).
  • Use +∞ for an interval unbounded to the right (e.g., (b, +∞) ).

You may assume the input list of planets can be in any order and may contain overlapping or nested gravitational ranges. Return the safe intervals in increasing order of start.