An array is monotonic if it is either monotone increasing or monotone decreasing.

An array nums is monotone increasing if for all i <= j, nums[i] <= nums[j]. An array nums is monotone decreasing if for all i <= j, nums[i] >= nums[j].

Given an integer array nums, return true if the given array is monotonic, or false otherwise.

Example 1:

Input: nums = [1,2,2,3]
Output: true
Example 2:

Input: nums = [6,5,4,4]
Output: true
Example 3:

Input: nums = [1,3,2]
Output: false
Example 4:

Input: nums = [1,2,4,5]
Output: true
Example 5:

Input: nums = [1,1,1]
Output: true

Constraints:

1 <= nums.length <= 105
-105 <= nums[i] <= 105