You are required to find an integer value target in an array arr of non-distinct integers. Before being passed as input to your search function, arr has been processed as follows:

• It has been sorted in non-descending order.

• It has been rotated around some pivot $k$, such that, after rotation, it looks like this: [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]]. For example, [10, 30, 40, 42, 42, 47, 78, 90, 901], rotated around pivot $k=5$ becomes [47, 78, 90, 901, 10, 30, 40, 42, 42].

Return TRUE if t exists in the rotated, sorted array arr, and FALSE otherwise, while minimizing the number of operations in the search.

Note: In this problem, the value of $k$ is not passed to your search function.

Constraints

• $1 \leq$ arr.length $\leq 1000$

• $-10^4 \leq$ arr[i] $\leq 10^4$

• arr is guaranteed to be rotated at some pivot index.

• $-10^4 \leq$ t $\leq 10^4$