An arbitrary array of integers $$$b$$$ of length $$$m$$$ is considered awesome if for all $$$i$$$ ($$$1 \le i \lt m$$$):

if $$$i$$$ is odd then $$$b_i \lt b_{i + 1}$$$ holds.
if $$$i$$$ is even then $$$b_i \gt b_{i + 1}$$$ holds.

In other words, the following inequality is true: $$$b_1 \lt b_2 \gt b_3 \lt b_4 \ldots$$$

You are given an array of positive integers $$$a$$$ of length $$$n$$$. You may do either of the following operations any number of times, in any order:

operation $$$1$$$: select an integer $$$i$$$ ($$$1 \le i \le n$$$) and do: $$$a_i := \max(a_1,\ldots,a_i)$$$, that is, replace $$$a_i$$$ with the prefix max up to $$$i$$$.
operation $$$2$$$: select an integer $$$i$$$ ($$$1 \le i \le n$$$) and then decrease $$$a_i$$$ by $$$1$$$.

Determine the minimum number of times you need to do operation $$$2$$$ to make $$$a$$$ awesome. Note that you do not need to minimise the number of times you perform operation $$$1$$$.

Input

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 an integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each testcase, output the minimum cost to make $$$a$$$ awesome.

Note

In the first test case, the array is already awesome so no operations need to be done.

In the second test case, $$$a$$$ can be made awesome as follows:

use operation $$$2$$$ and decrease $$$a_1$$$ by $$$1$$$. $$$[\color{red}3, 3, 2, 1] \rightarrow [\color{red}2, 3, 2, 1]$$$.
use operation $$$1$$$ and change $$$a_4$$$ to $$$\max(2, 3, 2, 1) = 3$$$. $$$[2, 3, 2, \color{red}1] \rightarrow [2, 3, 2, \color{red}3]$$$.

$$$[2, 3, 2, 3]$$$ is awesome as $$$2 \lt 3 \gt 2 \lt 3$$$. It can be proven that this is the minimum number of times operation $$$2$$$ needs to be performed.

Make it Zigzag

Examples