A13239 | 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.

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 15\ 000$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 3 \cdot 10^5$ ).

The second line of each test case contains a sequence of $n$ non-negative integers $a_1, \ldots, a_n$ ( $0 \le a_i \le 10^9$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$ .

For each test case, output a single line containing "Yes" (without quotes) if it's possible to make the given array sharpened using the described operations, or "No" (without quotes) otherwise.