#include <iostream> 
#include <string> 
#include <set> 
#include <map> 
#include <stack> 
#include <queue> 
#include <vector> 
#include <utility> 
#include <iomanip> 
#include <sstream> 
#include <bitset> 
#include <cstdlib> 
#include <iterator> 
#include <algorithm> 
#include <cstdio> 
#include <cctype> 
#include <cmath> 
#include <math.h> 
#include <ctime> 
#include <cstring> 
#include <unordered_set> 
#include <unordered_map> 
using namespace std;

#define sync {ios_base ::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);}
#define rep(n) for(int i = 0;i<n;i++)
#define rep1(a,b) for(int i = a;i<b;i++)
#define int long long int
#define mod 1000000007

int n;

int gcd(int a, int b)
{
    if (a == 0)
        return b;
    return gcd(b % a, a);
}

void solve()
{
    int n;
    cin>>n;
    int a[n];
    rep(n)
        cin>>a[i];
    
    
    int now = a[0];
    set<int> s;
    s.insert(now);
    bool poss=true;
    rep1(1,n)
    {
        if(a[i]==now){
            continue;
        }
        else 
        if(a[i]<now)
        {
            auto x=s.lower_bound(now);
            if(x==s.begin())
            {
                s.insert(a[i]);
            }
            else
            {
                x--;
                if(*x>a[i])
                {
                    poss=false;
                    break;
                }
                else
                {
                    s.insert(a[i]);
                }
            }
        }
        else
        {
            auto x = s.upper_bound(now);
            if(x==s.end())
            {
                s.insert(a[i]);
            }
            else
            {
                if(*x<a[i])
                {
                    poss=false;
                    break;
                }
                else
                {
                    s.insert(a[i]);
                }
            }
        }
        now = a[i];
    }
    if(poss)
    {
        cout<<"YES";
        return;
    }
    cout<<"NO";
}

int32_t main()
{

    #ifndef ONLINE_JUDGE
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif
    
    sync;
    int t = 1;
    cin>>t;
    while(t--){
        solve();
        cout<<"\n";
    }
    return 0;
}



### Prompt

In CPP, your task is to solve the following problem:

Uh oh! Ray lost his array yet again! However, Omkar might be able to help because he thinks he has found the OmkArray of Ray's array. The OmkArray of an array a with elements a_1, a_2, …, a_{2k-1}, is the array b with elements b_1, b_2, …, b_{k} such that b_i is equal to the median of a_1, a_2, …, a_{2i-1} for all i. Omkar has found an array b of size n (1 ≤ n ≤ 2 ⋅ 10^5, -10^9 ≤ b_i ≤ 10^9). Given this array b, Ray wants to test Omkar's claim and see if b actually is an OmkArray of some array a. Can you help Ray?

The median of a set of numbers a_1, a_2, …, a_{2i-1} is the number c_{i} where c_{1}, c_{2}, …, c_{2i-1} represents a_1, a_2, …, a_{2i-1} sorted in nondecreasing order. 

Input

Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

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

The second line contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9) — the elements of b.

It is guaranteed the sum of n across all test cases does not exceed 2 ⋅ 10^5. 

Output

For each test case, output one line containing YES if there exists an array a such that b_i is the median of a_1, a_2, ..., a_{2i-1} for all i, and NO otherwise. The case of letters in YES and NO do not matter (so yEs and No will also be accepted).

Examples

Input


5
4
6 2 1 3
1
4
5
4 -8 5 6 -7
2
3 3
4
2 1 2 3


Output


NO
YES
NO
YES
YES


Input


5
8
-8 2 -6 -5 -4 3 3 2
7
1 1 3 1 0 -2 -1
7
6 12 8 6 2 6 10
6
5 1 2 3 6 7
5
1 3 4 3 0


Output


NO
YES
NO
NO
NO

Note

In the second case of the first sample, the array [4] will generate an OmkArray of [4], as the median of the first element is 4.

In the fourth case of the first sample, the array [3, 2, 5] will generate an OmkArray of [3, 3], as the median of 3 is 3 and the median of 2, 3, 5 is 3.

In the fifth case of the first sample, the array [2, 1, 0, 3, 4, 4, 3] will generate an OmkArray of [2, 1, 2, 3] as 

  * the median of 2 is 2 
  * the median of 0, 1, 2 is 1 
  * the median of 0, 1, 2, 3, 4 is 2 
  * and the median of 0, 1, 2, 3, 3, 4, 4 is 3. 



In the second case of the second sample, the array [1, 0, 4, 3, 5, -2, -2, -2, -4, -3, -4, -1, 5] will generate an OmkArray of [1, 1, 3, 1, 0, -2, -1], as 

  * the median of 1 is 1 
  * the median of 0, 1, 4 is 1 
  * the median of 0, 1, 3, 4, 5 is 3 
  * the median of -2, -2, 0, 1, 3, 4, 5 is 1 
  * the median of -4, -2, -2, -2, 0, 1, 3, 4, 5 is 0 
  * the median of -4, -4, -3, -2, -2, -2, 0, 1, 3, 4, 5 is -2 
  * and the median of -4, -4, -3, -2, -2, -2, -1, 0, 1, 3, 4, 5, 5 is -1 



For all cases where the answer is NO, it can be proven that it is impossible to find an array a such that b is the OmkArray of a.

### Response

```cpp
#include <iostream> 
#include <string> 
#include <set> 
#include <map> 
#include <stack> 
#include <queue> 
#include <vector> 
#include <utility> 
#include <iomanip> 
#include <sstream> 
#include <bitset> 
#include <cstdlib> 
#include <iterator> 
#include <algorithm> 
#include <cstdio> 
#include <cctype> 
#include <cmath> 
#include <math.h> 
#include <ctime> 
#include <cstring> 
#include <unordered_set> 
#include <unordered_map> 
using namespace std;

#define sync {ios_base ::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);}
#define rep(n) for(int i = 0;i<n;i++)
#define rep1(a,b) for(int i = a;i<b;i++)
#define int long long int
#define mod 1000000007

int n;

int gcd(int a, int b)
{
    if (a == 0)
        return b;
    return gcd(b % a, a);
}

void solve()
{
    int n;
    cin>>n;
    int a[n];
    rep(n)
        cin>>a[i];
    
    
    int now = a[0];
    set<int> s;
    s.insert(now);
    bool poss=true;
    rep1(1,n)
    {
        if(a[i]==now){
            continue;
        }
        else 
        if(a[i]<now)
        {
            auto x=s.lower_bound(now);
            if(x==s.begin())
            {
                s.insert(a[i]);
            }
            else
            {
                x--;
                if(*x>a[i])
                {
                    poss=false;
                    break;
                }
                else
                {
                    s.insert(a[i]);
                }
            }
        }
        else
        {
            auto x = s.upper_bound(now);
            if(x==s.end())
            {
                s.insert(a[i]);
            }
            else
            {
                if(*x<a[i])
                {
                    poss=false;
                    break;
                }
                else
                {
                    s.insert(a[i]);
                }
            }
        }
        now = a[i];
    }
    if(poss)
    {
        cout<<"YES";
        return;
    }
    cout<<"NO";
}

int32_t main()
{

    #ifndef ONLINE_JUDGE
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif
    
    sync;
    int t = 1;
    cin>>t;
    while(t--){
        solve();
        cout<<"\n";
    }
    return 0;
}



```