There are $$$n$$$ cities in a row, numbered $$$1, 2, \ldots, n$$$ left to right.

- At time $$$1$$$, you conquer exactly one city, called the starting city.
- At time $$$2, 3, \ldots, n$$$, you can choose a city adjacent to the ones conquered so far and conquer it.

You win if, for each $$$i$$$, you conquer city $$$i$$$ at a time no later than $$$a_i$$$. A winning strategy may or may not exist, also depending on the starting city. How many starting cities allow you to win?

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of cities.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the deadlines for conquering the cities.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output a single integer: the number of starting cities that allow you to win.
Example Input 0:
3
6
6 3 3 3 5 5
6
5 6 4 1 4 5
9
8 6 4 2 1 3 5 7 9

Example Output 0:
3
0
1

Notes:
In the first test case, cities $$$2$$$, $$$3$$$, and $$$4$$$ are good starting cities.

In the second test case, there are no good starting cities.

In the third test case, the only good starting city is city $$$5$$$.

Example input:
3
6
6 3 3 3 5 5
6
5 6 4 1 4 5
9
8 6 4 2 1 3 5 7 9


Example output:
3
0
1