CF1291B Array Sharpening

You're given an array $ a_1, \ldots, a_n $ of $ n $ non-negative integers. Let's call it sharpened if and only if there exists an integer $ 1 \le k \le n $ such that $ a_1 < a_2 < \ldots < a_k $ and $ a_k > a_{k+1} > \ldots > a_n $ . In particular, any strictly increasing or strictly decreasing array is sharpened. For example: - The arrays $ [4] $ , $ [0, 1] $ , $ [12, 10, 8] $ and $ [3, 11, 15, 9, 7, 4] $ are sharpened; - The arrays $ [2, 8, 2, 8, 6, 5] $ , $ [0, 1, 1, 0] $ and $ [2, 5, 6, 9, 8, 8] $ are not sharpened. You can do the following operation as many times as you want: choose any strictly positive element of the array, and decrease it by one. Formally, you can choose any $ i $ ( $ 1 \le i \le n $ ) such that $ a_i>0 $ and assign $ a_i := a_i - 1 $ . Tell if it's possible to make the given array sharpened using some number (possibly zero) of these operations.

N/A

N/A

In the first and the second test case of the first test, the given array is already sharpened. In the third test case of the first test, we can transform the array into $ [3, 11, 15, 9, 7, 4] $ (decrease the first element $ 97 $ times and decrease the last element $ 4 $ times). It is sharpened because $ 3 < 11 < 15 $ and $ 15 > 9 > 7 > 4 $ . In the fourth test case of the first test, it's impossible to make the given array sharpened.