Pairing — Eolymp

Input

The first line contains three integers $n$ , $m$ , and $k$ ( $1 \leq n, m \leq 200$ 1 \le n,\, m \le 200, $1 \leq k \leq n \times m$ 1 \le k \le n \times m), representing the number of vertices in the first and second partitions, and the total number of edges, respectively. The following $k$ lines each contain two integers $a_{i}$ a_i and $b_{i}$ b_i, indicating an edge between vertex $a_{i}$ a_i in the first partition and vertex $b_{i}$ b_i in the second partition. Vertices in both partitions are numbered starting from one.

Output

On the first line, print a single integer $q$ - the maximum number of edges in the matching. On the second line, print $q$ integers - the indices of the edges that are part of the maximum matching. The edges are numbered starting from one, in the order they are given in the input.

Examples

Example 1

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