Sorted List With a Shift

Easy

A sensor logs readings in a ring: they were originally in non-decreasing order, but the log may have been read starting somewhere in the middle. In other words, a sorted list may have been rotated by some number of positions (possibly zero): a few leading elements moved to the end, keeping their order. Given the list readings, return True if it can be such a rotation of a list sorted in non-decreasing order, and False otherwise. Readings may repeat.

Example 1

readings=[6, 8, 8, 2, 3] → True

The original order was [2, 3, 6, 8, 8]; its beginning was simply moved to the end.

Example 2

readings=[5, 1, 4, 2] → False

Values drop both after 5 and after 4, which no shift of a sorted list can produce.

Example 3

readings=[1, 2, 9] → True

The list is already sorted, which is a shift by zero positions.

Constraints

1 ≤ len(readings) ≤ 100
1 ≤ readings[i] ≤ 100

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Topics

Array

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Input

readings=[6, 8, 8, 2, 3]

Expected

True

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