Maximum Smaller

You are given an array A

A of size N

N.

The score of a permutation P

P of the integers [1,N]

[1,N] is defined as follows:

• If Pi=i
• 
  
• Pi
• ​=i for at least one i
• 
  
• i (1≤i≤N
• 
  
• 1≤i≤N), the score is −1
• 
  
• −1.
• Otherwise, the score is the number of indices i
• 
  
• i (1≤i≤N
• 
  
• 1≤i≤N) such that APi≤Ai
• 
  
• APi
• ​
• ​≤Ai
• ​.

Find the maximum possible score for some permutation P

P. You also need to print a valid permutation.

Input Format

• The first line of input will contain a single integer T
• 
  
• T, denoting the number of test cases.
• Each test case consists of multiple lines of input.
• The first line of each test case contains a single integer N
• 
  
• N - the size of the array.
• The second line contains N
• 
  
• N integers - A1,A2,…,AN
• 
  
• A1
• ​,A2
• ​,…,AN
• ​.

Output Format

For each test case, output the following:

• On a new line, first output the maximum possible score.
• Next, output N
• 
  
• N integers, P1,P2,…,PN
• 
  
• P1
• ​,P2
• ​,…,PN
• ​, any valid permutation that obtains the maximum score.

If multiple answers are possible, all will be accepted.

Constraints

• 1≤T≤104
• 
  
• 1≤T≤104
• 2≤N≤2⋅105
• 
  
• 2≤N≤2⋅105
• 1≤Ai≤N
• 
  
• 1≤Ai
• ​≤N
• The sum of N
• 
  
• N over all test cases does not exceed 2⋅105
• 
  
• 2⋅105
• .

Sample 1:

Input

Output

3 3 1 1 1 3 3 1 2 2 2 2
3 2 3 1 2 3 1 2 2 2 1

Explanation:

Test Case 1 : Any permutation P

P which does not have Pi=i

Pi

​=i for any index i

i, would have a score of 3

3 because all values are 1

1, so APi≤Ai

APi

​

​≤Ai

​ always holds.

Test Case 2 : P=[3,1,2]

P=[3,1,2] means that index i=1,3

i=1,3 are good because AP1=A3=2≤A1

AP1

​

​=A3

​=2≤A1

​, and AP3=A2=1≤A3

AP3

​

​=A2

​=1≤A3

​. It can be shown that a larger score is impossible.