# Strahler Order

# Strahler Order

In geology, a river system can be represent as a direct graph. Each river segment is an edge; with the edge pointing the same way the waters flows. Nodes are either the source of a river segment (for example, a lake or spring), where rivers segments merge of diverge, or the mouth of the river.

The *Strahler order* of a river system is computed as follows.

- The order of each source node is
**1**. - For every other node, let
**i**be the highest order of all its upstream nodes. If just one upstream node has order**i**, then this node also has order**i**. If two or more upstream nodes have order**i**, then this node has order**i**+**1**.

The order of the entire river system is the order of the mouth node. In this problem, the river system will have just one mouth. In the picture above, The *Strahler* order is three (3).

The number in a box is the order. The number in a circle is the node number.

You must write a program to determine the order of a given river system.

The actual river with the highest order is the *Amazon*, with order **12**. The highest in the U.S. is the Mississippi, width order **10**.

#### Input

The first line contains the number **t** (**1** ≤ **t** ≤ **1000**) of data sets that follow. Each data set should be processed independently.

Each data set consists of multiple lines. The first line of each data set contains three positive integers **k**, **m** and **p** (**2** ≤ **m** ≤ **1000**). **k** is the data set number. **m** is the number of nodes in the graph and **p** is the number of edges. The first line is followed by **p** lines, each describing an edge of the graph. The line will contain two positive integers **a** and **b**, indicating that water flows from node **a** to node **b** (**1** ≤ **a**, **b** ≤ **m**). Node **m** is the mouth of the river. It has no outgoing edges.

#### Output

For each data set there is a single line of output. The line consists o the data set number, a single space and the order of the river system.

1 1 7 8 1 3 2 3 6 4 3 4 3 5 6 7 5 7 4 7

1 3