Given an array A of size N, construct a simple (i.e, without self-loops and multiedges) strongly connected directed graph with N nodes where A_{i} denotes the colour of i^{th} node.

The graph should satisfy the following properties:
If A_{i} = A_{j}, then nodes i and j should have the same outdegree.
If A_{i} = A_{j}, neither of the edges $i \to$ j and $j \to$ i should exist.
If the edge $u \to$ v exists, then the edge $v \to$ u cannot exist.
Under the above conditions, the number of edges should be maximized.

Note:
It is guaranteed that A contains at least 2 distinct elements.
If A contains K distinct elements, they will be the integers $0, 1, 2, \ldots, K-1$.

Find any graph that satisfies the above conditions.
If no such graph exists, print -1 instead.

------ Input Format ------

• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of two lines of input.
• The first line of each test consists of a single integer N, denoting the number of nodes in the graph.
• The second line contains $N space-separated integers A_{1},A_{2},\ldots,A_{N}$, where A_{i} denotes the colour of i-th node.

------ Output Format ------

For each test case,
- If no valid graph exists, output -1 on a new line.
- Otherwise, first output on a new line M: the maximum number of edges in such a graph.
- Then, output M lines, each containing two space-separated integers u and v, denoting an edge from u to v.

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 1000$
$0 ≤ A_{i} < K$, where $K$ is the number of distinct elements in $A$.
- The sum of $N$ over all test cases won't exceed $1000$.

----- Sample Input 1 ------
3
4
1 0 1 0
5
0 1 2 3 4
3
0 1 1
----- Sample Output 1 ------
4
1 2
3 4
4 1
2 3
10
1 2
2 3
2 4
2 5
3 1
3 4
3 5
4 1
4 5
5 1
-1
----- explanation 1 ------
Test case $1$: Nodes $1$ and $3$ are colored $1$, and nodes $2$ and $4$ are colored $0$.
The out degree of nodes $[1,3]$ is $1$ and out degree of nodes $[2,4]$ is also $1$, and the graph is strongly connected.

Test case $2$: Every node has a distinct color, so those conditions are automatically satisfied. $10$ edges is also the maximum possible number of edges such a graph can have.

见题面

见题面