Tree

A tree is a graph with the following three properties.

1. It is connected. Starting from any node you can reach every other node along edges.
2. Removing one edge breaks the connection. Some node can no longer be reached.
3. Adding one edge between two existing nodes A and B creates a cycle. A cycle exists when there is more than one way to get from A to B.

Given a graph, decide whether it is a tree.

The first line contains an integer $T$, the number of graphs to check. $T$ is at most 10.

Each graph is given in the following format.

The first line contains the number of nodes $N$, where $1 \le N \le 1000$. The nodes are numbered from 1 to $N$.

The next line contains the number of edges $M$, where $0 \le M \le 10^6$.

The next $M$ lines each contain two integers $A$ and $B$, the two nodes that one edge connects. $A$ and $B$ can be equal, and the same pair can appear more than once.

The sum of $M$ over all graphs is at most $10^6$.

For each graph, print one line: tree if the graph is a tree, and graph otherwise.