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

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

Return true if and only if the given array A is monotonic.

Example 1:

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

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

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

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

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

Note:

1 <= A.length <= 50000 -100000 <= A[i] <= 100000