Grand Prix

Time Limit: 4 Seconds

Memory Limit: 65536 KB

Description

A new season of Touhou M-1 Grand Prix is approaching. Girls in Gensokyo cannot wait for participating it. Before the registration, they have to decide which combination they are going to compete as. Every girl in Gensokyo is either a boke (funny girl) or a tsukomi (straight girl). Every candidate combination is made up of a boke and a tsukomi. A girl may belong to zero or more candidate combinations, but one can only register as a member of one formal combination. The host of Touhou M-1 Grand Prix hopes that as many formal combinations as possible can participate in this year. Under these constraints, some candidate combinations are actually redundant as it's impossible to register it as a formal one as long as the number of formal combinations has to be maximized. So they want to figure out these redundant combinations and stop considering about them.

Input

There are multiple test cases. Process to the End of File.

The first line of each test case contains three integers: 1 ≤ X, Y ≤ 20,000 and 1 ≤ M ≤ 100,000, where X and Y are the number of boke girls and the number of tsukomi girls in Gensokyo, and M is the number of candidate combinations.

The following M lines are M different candidate combinations, one by each line. Each combination is represented by a 6-digit 32-based number, where the first 3 digits represents the index 0 ≤ Bi < X of the boke girl, the last 3 digit represents the index 0 ≤ Ti < Y of the tsukomi girl. A 32-based number uses the 10 decimal digits, '0' through '9', and the first 22 letters of the alphabet, 'A' through 'V', as 32-based digits. For example, 32-based number AVI is 11250 in decimal form.

Output

For each test case, output the number of redundant combinations in the first line. Then output the space-separated zero-based indexes of the redundant combinations in ascending order in the second line.

Sample Input

2 2 3
000001
001001
001000
3 3 6
000000
001000
001001
002000
002001
002002


Sample Output

1
1
3
1 3 4


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