Algorithm


E1. Permutation Minimization by Deque
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.

A permutation p of size n is given. A permutation of size n is an array of size n in which each integer from 11 to n occurs exactly once. For example, [1,4,3,2][1,4,3,2] and [4,2,1,3][4,2,1,3] are correct permutations while [1,2,4][1,2,4] and [1,2,2][1,2,2] are not.

Let us consider an empty deque (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements [1,5,2][1,5,2] currently in the deque, adding an element 44 to the beginning will produce the sequence [4,1,5,2][4,1,5,2], and adding same element to the end will produce [1,5,2,4][1,5,2,4].

The elements of the permutation are sequentially added to the initially empty deque, starting with p1�1 and finishing with pn��. Before adding each element to the deque, you may choose whether to add it to the beginning or the end.

For example, if we consider a permutation p=[3,1,2,4]�=[3,1,2,4], one of the possible sequences of actions looks like this:

 1. add 33 to the end of the deque: deque has a sequence [3][3] in it;
 2. add 11 to the beginning of the deque: deque has a sequence [1,3][1,3] in it;
 3. add 22 to the end of the deque: deque has a sequence [1,3,2][1,3,2] in it;
 4. add 44 to the end of the deque: deque has a sequence [1,3,2,4][1,3,2,4] in it;

 

Find the lexicographically smallest possible sequence of elements in the deque after the entire permutation has been processed.

A sequence [x1,x2,,xn][�1,�2,…,��] is lexicographically smaller than the sequence [y1,y2,,yn][�1,�2,…,��] if there exists such in�≤� that x1=y1�1=�1x2=y2�2=�2xi1=yi1��−1=��−1 and xi<yi��<��. In other words, if the sequences x and y have some (possibly empty) matching prefix, and the next element of the sequence x is strictly smaller than the corresponding element of the sequence y. For example, the sequence [1,3,2,4][1,3,2,4] is smaller than the sequence [1,3,4,2][1,3,4,2] because after the two matching elements [1,3][1,3] in the start the first sequence has an element 22 which is smaller than the corresponding element 44 in the second sequence.

Input

The first line contains an integer t (1t10001≤�≤1000) — the number of test cases.

The next 2t2� lines contain descriptions of the test cases.

The first line of each test case description contains an integer n (1n21051≤�≤2⋅105) — permutation size. The second line of the description contains n space-separated integers pi�� (1pin1≤��≤�; all pi�� are all unique) — elements of the permutation.

It is guaranteed that the sum of n over all test cases does not exceed 21052⋅105.

Output

Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should contain n space-separated integer numbers — the elements of the lexicographically smallest permutation that is possible to find in the deque after executing the described algorithm.

Example
input
Copy
5
4
3 1 2 4
3
3 2 1
3
3 1 2
2
1 2
2
2 1
output
Copy
1 3 2 4 
1 2 3 
1 3 2 
1 2 
1 2 
Note

One of the ways to get a lexicographically smallest permutation [1,3,2,4][1,3,2,4] from the permutation [3,1,2,4][3,1,2,4] (the first sample test case) is described in the problem statement.

 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include<bits/stdc++.h>
using namespace std;

int main(){
  int t;
  cin>>t;

  int n;
  while(t--){
    deque <int> deqs;
    cin>>n;
    int x;
    for(int i = 0; i < n;i++){
      cin>>x;
      if(x > deqs.front()){
        deqs.push_back(x);
        continue;
      }
      deqs.push_front(x);
    }
    for(int i = 0; i < n; i++){
      cout<<deqs.at(i)<<" ";
    }
    cout<<endl;
  }
}
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Input

x
+
cmd
5
4
3 1 2 4
3
3 2 1
3
3 1 2
2
1 2
2
2 1

Output

x
+
cmd
1 3 2 4
1 2 3
1 3 2
1 2
1 2
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Demonstration


Codeforcess Solution 1579-E1 E1. Permutation Minimization by Deque ,C++, Java, Js and Python ,1579-E1,Codeforcess Solution

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