Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

You are given $K$ permutations of integers $1$ through $N$. For each $i$ ($1 ≤ i ≤ K$), the $i$-th permutation is denoted by $A_{i,1}, A_{i,2}, \ldots, A_{i,N}$.

Construct a directed acyclic graph with $N$ nodes (numbered $1$ through $N$) such that:
Each of the given permutations is a valid topological sort of the graph. Formally, for each valid $k$ and each $i, j$ ($1 ≤ i < j ≤ N$), there is no edge from the node $A_{k,j}$ to the node $A_{k,i}$.
The outdegree of each node is at most $1$.
The number of nodes with indegree $0$ is the smallest possible.

If there are multiple solutions, you may find any one.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains two space-separated integers $N$ and $K$.
$K$ lines follow. For each $i$ ($1 ≤ i ≤ K$), the $i$-th of these lines contains $N$ space-separated integers $A_{i,1}, A_{i,2}, \ldots, A_{i,N}$.

------ Output ------
For each test case, print two lines.
The first of these lines should contain one integer ― the minimum number of nodes with indegree $0$.
The second line should contain $N$ space-separated integers $v_{1}, v_{2}, \ldots, v_{N}$ describing your graph in the following way: for each valid $i$, if $v_{i} = 0$, there is no outgoing edge from the $i$-th node; otherwise, there is an edge from the $i$-th node to the $v_{i}$-th node.

------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 500$
$1 ≤ K ≤ 100$
$1 ≤ A_{i,j} ≤ N$ for each valid $i,j$
the sum of $N$ over all test cases does not exceed $2,000$

------ Subtasks ------
Subtask #1 (20 points):
$N ≤ 20$
$K ≤ 10$

Subtask #2 (80 points): original constraints

----- Sample Input 1 ------
2

2 2

1 2

2 1

2 2

1 2

1 2
----- Sample Output 1 ------
2

0 0

1

2 0
----- explanation 1 ------
Example case 1: The graph must consist of just two disconnected nodes, since no edges are allowed. Hence, there are two nodes with indegree $0$.

Example case 2: The graph may contain an edge from node $1$ to node $2$. Then, there is only one node with indegree $0$.

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