Statement

Given an array P, which is initially a permutation of the numbers 0, 1, …, N - 1. You can do the remove a valley operation on P: (1) select an index i (0 < i < |P| - 1) such that P_i < P_i - 1 and P_i < P_i + 1. (2) then, remove P_i from P. where |P| is the number of elements of the array P (which is initially N). Notice that after performing the operation, the number of elements of P will decrease by 1. Find the minimum number of times you need to remove a valley such that P becomes a mountain, i.e. firstly increasing, and then decreasing. Formally: there should exist an i such that 0 < i < |P| - 1 and P_j < P_j + 1 for each j < i and P_k - 1 > P_k for each k > i).