#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define M 998244353
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define pie acos(-1)
#define loop(i,a,n) for(int i=a;i<n;i++)
#define trav(a,x) for(auto &a:x)
#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define pll pair<ll,ll>
#define pii pair<int,int>
#define endl "\n"
#define debug(x)  cout<<#x<<" " <<x<<endl;
#define dbg(x,y)  cout<<#x<<" " <<x<<" "<<#y<<" "<<y<<endl;
#define all(v) v.begin(),v.end()
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t,h=0;
    cin>>t;
    while(t--)
    {
         h++;
     string s;
     ll n,k,x;
     cin>>n;
     vl a; 
     ll ans=0;
    loop(i,0,n){
              cin>>x;
              a.pb(x);
        }
        ans=2*n-1;
        for(ll i=0;i<(n-2);i++){
             if(a[i]<a[i+1]&&a[i+1]>a[i+2])ans++;
             if(a[i]>a[i+1]&&a[i+1]<a[i+2])ans++;
        }
        for(ll i=0;i<(n-3);i++){
             if(a[i]<a[i+1]&&a[i+1]>a[i+2]){
                  if(a[i+2]<a[i]&&a[i+3]>a[i+2]&&a[i+3]<a[i+1])ans++;
             }
             if(a[i]>a[i+1]&&a[i+1]<a[i+2]){
                  if(a[i+2]>a[i]&&a[i+3]<a[i+2]&&a[i+3]>a[i+1])ans++;
             }
        }
        cout<<ans<<endl;
    }
	return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

Suppose you have two points p = (x_p, y_p) and q = (x_q, y_q). Let's denote the Manhattan distance between them as d(p, q) = |x_p - x_q| + |y_p - y_q|.

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

Let's say that an array b_1, b_2, ..., b_m is good if it is impossible to choose three distinct indices i, j, k such that the points (b_i, i), (b_j, j) and (b_k, k) form a bad triple.

You are given an array a_1, a_2, ..., a_n. Calculate the number of good subarrays of a. A subarray of the array a is the array a_l, a_{l + 1}, ..., a_r for some 1 ≤ l ≤ r ≤ n.

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

Input

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

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

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

It's guaranteed that the sum of n doesn't exceed 2 ⋅ 10^5.

Output

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

Example

Input


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


Output


10
12
3

Note

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

  * d((a_2, 2), (a_4, 4)) = |4 - 3| + |2 - 4| = 3 < d((a_2, 2), (a_3, 3)) + d((a_3, 3), (a_4, 4)) = 3 + 1 + 2 + 1 = 7; 
  * d((a_2, 2), (a_3, 3)) < d((a_2, 2), (a_4, 4)) + d((a_4, 4), (a_3, 3)); 
  * d((a_3, 3), (a_4, 4)) < d((a_3, 3), (a_2, 2)) + d((a_2, 2), (a_4, 4)); 



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

  * d((a_1, 1), (a_4, 4)) = |6 - 9| + |1 - 4| = 6; 
  * d((a_1, 1), (a_2, 2)) = |6 - 9| + |1 - 2| = 4; 
  * d((a_2, 2), (a_4, 4)) = |9 - 9| + |2 - 4| = 2; 



So, d((a_1, 1), (a_4, 4)) = d((a_1, 1), (a_2, 2)) + d((a_2, 2), (a_4, 4)).

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define M 998244353
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define pie acos(-1)
#define loop(i,a,n) for(int i=a;i<n;i++)
#define trav(a,x) for(auto &a:x)
#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define pll pair<ll,ll>
#define pii pair<int,int>
#define endl "\n"
#define debug(x)  cout<<#x<<" " <<x<<endl;
#define dbg(x,y)  cout<<#x<<" " <<x<<" "<<#y<<" "<<y<<endl;
#define all(v) v.begin(),v.end()
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t,h=0;
    cin>>t;
    while(t--)
    {
         h++;
     string s;
     ll n,k,x;
     cin>>n;
     vl a; 
     ll ans=0;
    loop(i,0,n){
              cin>>x;
              a.pb(x);
        }
        ans=2*n-1;
        for(ll i=0;i<(n-2);i++){
             if(a[i]<a[i+1]&&a[i+1]>a[i+2])ans++;
             if(a[i]>a[i+1]&&a[i+1]<a[i+2])ans++;
        }
        for(ll i=0;i<(n-3);i++){
             if(a[i]<a[i+1]&&a[i+1]>a[i+2]){
                  if(a[i+2]<a[i]&&a[i+3]>a[i+2]&&a[i+3]<a[i+1])ans++;
             }
             if(a[i]>a[i+1]&&a[i+1]<a[i+2]){
                  if(a[i+2]>a[i]&&a[i+3]<a[i+2]&&a[i+3]>a[i+1])ans++;
             }
        }
        cout<<ans<<endl;
    }
	return 0;
}

```