Longest Calm Stretch

A weather station logs the wind speed once a minute, and readings[i] is the i-th reading. A stretch of consecutive readings is calm when its highest reading minus its lowest reading is at most limit.

Write longest_calm(readings, limit) that returns the length of the longest calm stretch, or 0 if there are no readings.

Examples

longest_calm([12, 15, 11, 30, 28, 33, 29, 27], 6)   # returns 5
longest_calm([3, 9, 4, 6, 5, 12], 3)               # returns 3
longest_calm([5, 5, 5, 5], 0)                       # returns 4

In the first example the stretch 30, 28, 33, 29, 27 is calm: its highest reading is 33 and its lowest is 27, a difference of 6.

Constraints

• 0 <= len(readings) <= 100,000
• 0 <= readings[i] <= 10^9
• 0 <= limit <= 10^9

Note

Working out the highest and lowest reading of every stretch from scratch is far too slow for 100,000 readings.