Codeforces Round #717 (Div. 2)-C. Baby Ehab Partitions Again-题解

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目录

Educational Codeforces Round 111 (Rated for Div. 2)-C. Manhattan Subarrays

传送门
Time Limit: 2 seconds
Memory Limit: 256 megabytes

Problem Description

Suppose you have two points p = ( x p , y p ) p = (x_p, y_p) p=(xp​,yp​) and q = ( x q , y q ) q = (x_q, y_q) q=(xq​,yq​). Let’s denote the Manhattan distance between them as d ( p , q ) = ∣ x p − x q ∣ + ∣ y p − y q ∣ d(p, q) = |x_p - x_q| + |y_p - y_q| d(p,q)=∣xp​−xq​∣+∣yp​−yq​∣.

Let’s say that three points p p p, q q q, r r r form a bad triple if d ( p , r ) = d ( p , q ) + d ( q , r ) d(p, r) = d(p, q) + d(q, r) d(p,r)=d(p,q)+d(q,r).

Let’s say that an array b 1 , b 2 , … , b m b_1, b_2, \\dots, b_m b1​,b2​,…,bm​ is good if it is impossible to choose three distinct indices i i i, j j j, k k k such that the points ( b i , i ) (b_i, i) (bi​,i), ( b j , j ) (b_j, j) (bj​,j) and ( b k , k ) (b_k, k) (bk​,k) form a bad triple.

You are given an array a 1 , a 2 , … , a n a_1, a_2, \\dots, a_n a1​,a2​,…,an​. Calculate the number of good subarrays of a a a. A subarray of the array a a a is the array a l , a l + 1 , … , a r a_l, a_{l + 1}, \\dots, a_r al​,al+1​,…,ar​ for some 1 ≤ l ≤ r ≤ n 1 \\le l \\le r \\le n 1≤l≤r≤n.

Note that, according to the definition, subarrays of length 1 1 1 and 2 2 2 are good.

Input

The first line contains one integer t t t ( 1 ≤ t ≤ 5000 1 \\le t \\le 5000 1≤t≤5000) — the number of test cases.

The first line of each test case contains one integer n n n ( 1 ≤ n ≤ 2 ⋅ 1 0 5 1 \\le n \\le 2 \\cdot 10^5 1≤n≤2⋅105) — the length of array a a a.

The second line of each test case contains n n n integers a 1 , a 2 , … , a n a_1, a_2, \\dots, a_n a1​,a2​,…,an​ ( 1 ≤ a i ≤ 1 0 9 1 \\le a_i \\le 10^9 1≤ai​≤109).

It’s guaranteed that the sum of n n n doesn’t exceed 2 ⋅ 1 0 5 2 \\cdot 10^5 2⋅105.

Output

For each test case, print the number of good subarrays of array a a a.

Sample Input

3
4
2 4 1 3
5
6 9 1 9 6
2
13 37

Sample Onput

10
12
3

Note

In the first test case, it can be proven that any subarray of a a a is good. For example, subarray [ a 2 , a 3 , a 4 ] [a_2, a_3, a_4] [a2​,a3​,a4​] is good since it contains only three elements and:

In the second test case, for example, subarray [ a 1 , a 2 , a 3 , a 4 ] [a_1, a_2, a_3, a_4] [a1​,a2​,a3​,a4​] is not good, since it contains a bad triple ( a 1 , 1 ) (a_1, 1) (a1​,1), ( a 2 , 2 ) (a_2, 2) (a2​,2), ( a 4 , 4 ) (a_4, 4) (a4​,4):

So, d ( ( a 1 , 1 ) , ( a 4 , 4 ) ) = d ( ( a 1 , 1 ) , ( a 2 , 2 ) ) + d ( ( a 2 , 2 ) , ( a 4 , 4 ) ) d((a_1, 1), (a_4, 4)) = d((a_1, 1), (a_2, 2)) + d((a_2, 2), (a_4, 4)) d((a1​,1),(a4​,4))=d((a1​,1),(a2​,2))+d((a2​,2),(a4​,4)).

题目大意

给你 n n n个数，问你这 n n n个数组成的序列中，有多少个子序列（连续）满足：