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.
﻿#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <fstream>
//#include <sstream>
#include <vector>
#include <set>
#include <string>
#include <cmath>
#include <algorithm>
#include <map>
#include <queue>
#include <iomanip>
#include <cstring>
#include <stdio.h>
#include <cassert>
using namespace std;



void solve() {
	int n;
	cin >> n;
	vector<int>all(n);
	for (int i = 0; i < n; i++)
		cin >> all[i];
	if (n == 1) {
		cout << "YES" << '\n';
		return;
	}
	set<int>f;
	f.insert(all[0]);
	for (int i = 1; i < n; i++) {
		if (all[i] == all[i - 1]) {
			f.insert(all[i]);
			continue;
		}
		if (all[i] > all[i - 1]) {
			if (*f.rbegin() > all[i - 1]) {
				int x = *f.upper_bound(all[i - 1]);
				if (x < all[i]) {
					cout << "NO" << '\n';
					return;
				}
			}
		}
		if (all[i] < all[i - 1]) {
			if (*f.rbegin() > all[i]) {
				int x = *f.upper_bound(all[i]);
				if (x < all[i - 1]) {
					cout << "NO" << '\n';
					return;
				}
			}
		}
		f.insert(all[i]);
	}
	cout << "YES" << '\n';
}

int main() {
	#ifdef _DEBUG
		freopen("input.txt", "r", stdin);
		freopen("output.txt", "w", stdout);
	#endif // _DEBUG
	int t;
	cin >> t;
	//t = 1;
	while (t) {
		t--;
		solve();
	}
}