B2. Range Sorting (Hard Version)
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The only difference between this problem and the easy version is the constraints on $$$t$$$ and $$$n$$$.

You are given an array $$$a$$$, consisting of $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$.

Define the beauty of an array $$$p_1, p_2, \ldots p_k$$$ as the minimum amount of time needed to sort this array using an arbitrary number of range-sort operations. In each range-sort operation, you will do the following:

  • Choose two integers $$$l$$$ and $$$r$$$ ($$$1 \le l < r \le k$$$).
  • Sort the subarray $$$p_l, p_{l + 1}, \ldots, p_r$$$ in $$$r - l$$$ seconds.

Please calculate the sum of beauty over all subarrays of array $$$a$$$.

A subarray of an array is defined as a sequence of consecutive elements of the array.

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 a single integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — the length of the array $$$a$$$.

The second line of each test case consists of $$$n$$$ integers $$$a_1,a_2,\ldots, a_n$$$ ($$$1\le a_i\le 10^9$$$). It is guaranteed that all elements of $$$a$$$ are pairwise distinct.

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

Output

For each test case, output the sum of beauty over all subarrays of array $$$a$$$.

Example
Input
5
2
6 4
3
3 10 6
4
4 8 7 2
5
9 8 2 4 6
12
2 6 13 3 15 5 10 8 16 9 11 18
Output
1
2
8
16
232
Note

In the first test case:

  • The subarray $$$[6]$$$ is already sorted, so its beauty is $$$0$$$.
  • The subarray $$$[4]$$$ is already sorted, so its beauty is $$$0$$$.
  • You can sort the subarray $$$[6, 4]$$$ in one operation by choosing $$$l = 1$$$ and $$$r = 2$$$. Its beauty is equal to $$$1$$$.
The sum of beauty over all subarrays of the given array is equal to $$$0 + 0 + 1 = 1$$$.

In the second test case:

  • The subarray $$$[3]$$$ is already sorted, so its beauty is $$$0$$$.
  • The subarray $$$[10]$$$ is already sorted, so its beauty is $$$0$$$.
  • The subarray $$$[6]$$$ is already sorted, so its beauty is $$$0$$$.
  • The subarray $$$[3, 10]$$$ is already sorted, so its beauty is $$$0$$$.
  • You can sort the subarray $$$[10, 6]$$$ in one operation by choosing $$$l = 1$$$ and $$$r = 2$$$. Its beauty is equal to $$$2 - 1 = 1$$$.
  • You can sort the subarray $$$[3, 10, 6]$$$ in one operation by choosing $$$l = 2$$$ and $$$r = 3$$$. Its beauty is equal to $$$3 - 2 = 1$$$.
The sum of beauty over all subarrays of the given array is equal to $$$0 + 0 + 0 + 0 + 1 + 1 = 2$$$.