You have $$$2n$$$ integers $$$1, 2, \dots, 2n$$$. You have to redistribute these $$$2n$$$ elements into $$$n$$$ pairs. After that, you choose $$$x$$$ pairs and take minimum elements from them, and from the other $$$n - x$$$ pairs, you take maximum elements.

Your goal is to obtain the set of numbers $$$\{b_1, b_2, \dots, b_n\}$$$ as the result of taking elements from the pairs.

What is the number of different $$$x$$$-s ($$$0 \le x \le n$$$) such that it's possible to obtain the set $$$b$$$ if for each $$$x$$$ you can choose how to distribute numbers into pairs and from which $$$x$$$ pairs choose minimum elements?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

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

The second line of each test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_1 \lt b_2 \lt \dots \lt b_n \le 2n$$$) — the set you'd like to get.

It's guaranteed that the sum of $$$n$$$ over test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print one number — the number of different $$$x$$$-s such that it's possible to obtain the set $$$b$$$.

Note

In the first test case, $$$x = 1$$$ is the only option: you have one pair $$$(1, 2)$$$ and choose the minimum from this pair.

In the second test case, there are three possible $$$x$$$-s. If $$$x = 1$$$, then you can form the following pairs: $$$(1, 6)$$$, $$$(2, 4)$$$, $$$(3, 5)$$$, $$$(7, 9)$$$, $$$(8, 10)$$$. You can take minimum from $$$(1, 6)$$$ (equal to $$$1$$$) and the maximum elements from all other pairs to get set $$$b$$$.

If $$$x = 2$$$, you can form pairs $$$(1, 2)$$$, $$$(3, 4)$$$, $$$(5, 6)$$$, $$$(7, 9)$$$, $$$(8, 10)$$$ and take the minimum elements from $$$(1, 2)$$$, $$$(5, 6)$$$ and the maximum elements from the other pairs.

If $$$x = 3$$$, you can form pairs $$$(1, 3)$$$, $$$(4, 6)$$$, $$$(5, 7)$$$, $$$(2, 9)$$$, $$$(8, 10)$$$ and take the minimum elements from $$$(1, 3)$$$, $$$(4, 6)$$$, $$$(5, 7)$$$.

In the third test case, $$$x = 0$$$ is the only option: you can form pairs $$$(1, 3)$$$, $$$(2, 4)$$$ and take the maximum elements from both of them.

Pairs

Examples