Let $$$p_1, \ldots, p_n$$$ be a permutation of $$$[1, \ldots, n]$$$.

Let the $$$q$$$-subsequence of $$$p$$$ be a permutation of $$$[1, q]$$$, whose elements are in the same relative order as in $$$p_1, \ldots, p_n$$$. That is, we extract all elements not exceeding $$$q$$$ together from $$$p$$$ in the original order, and they make the $$$q$$$-subsequence of $$$p$$$.

For a given array $$$a$$$, let $$$pre(i)$$$ be the largest value satisfying $$$pre(i) \lt i$$$ and $$$a_{pre(i)} \gt a_i$$$. If it does not exist, let $$$pre(i) = -10^{100}$$$. Let $$$nxt(i)$$$ be the smallest value satisfying $$$nxt(i) \gt i$$$ and $$$a_{nxt(i)} \gt a_i$$$. If it does not exist, let $$$nxt(i) = 10^{100}$$$.

For each $$$q$$$ such that $$$1 \leq q \leq n$$$, let $$$a_1, \ldots, a_q$$$ be the $$$q$$$-subsequence of $$$p$$$. For each $$$i$$$ such that $$$1 \leq i \leq q$$$, $$$pre(i)$$$ and $$$nxt(i)$$$ will be calculated as defined. Then, you will be given some integer values of $$$x$$$, and for each of them you have to calculate $$$\sum\limits_{i=1}^q \min(nxt(i) - pre(i), x)$$$.

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 $$$n$$$ ($$$1 \leq n \leq 3\cdot 10^5$$$) — the length of the permutation.

The second line of each test case contains $$$n$$$ integers $$$p_1, \ldots, p_n$$$ ($$$1 \leq p_i \leq n$$$) — the initial permutation.

Then, for each $$$q$$$ such that $$$1 \leq q \leq n$$$ in ascending order, you will be given an integer $$$k$$$ ($$$0 \leq k \leq 10^5$$$), representing the number of queries for the $$$q$$$-subsequence. Then $$$k$$$ numbers in a line follow: each of them is the value of $$$x$$$ for a single query ($$$1 \leq x \leq q$$$).

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

Output

For each test case, for each query, print a single line with an integer: the answer to the query.

Note

The $$$1$$$-subsequence is $$$[1]$$$, and $$$pre=[-10^{100}]$$$, $$$nxt=[10^{100}]$$$. $$$ans(1)=\min(10^{100}-(-10^{100}),1)=1$$$.

The $$$5$$$-subsequence is $$$[1,4,3,2,5]$$$, and $$$pre=[-10^{100},-10^{100},2,3,-10^{100}]$$$, $$$nxt=[2,5,5,5,10^{100}]$$$. $$$ans(1)=5,ans(2)=10,ans(3)=14$$$.

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