Valera has got a rectangle table consisting of n rows and m columns. Valera numbered the table rows starting from one, from top to bottom and the columns – starting from one, from left to right. We will represent cell that is on the intersection of row x and column y by a pair of integers (x, y).
Valera wants to place exactly k tubes on his rectangle table. A tube is such sequence of table cells (x_{1}, y_{1}), (x_{2}, y_{2}), ..., (x_{r}, y_{r}), that:
Valera thinks that the tubes are arranged in a fancy manner if the following conditions are fulfilled:
Help Valera to arrange k tubes on his rectangle table in a fancy manner.
The first line contains three space-separated integers n, m, k (2 ≤ n, m ≤ 300; 2 ≤ 2k ≤ n·m) — the number of rows, the number of columns and the number of tubes, correspondingly.
Print k lines. In the i-th line print the description of the i-th tube: first print integer r_{i} (the number of tube cells), then print 2r_{i} integers x_{i1}, y_{i1}, x_{i2}, y_{i2}, ..., x_{iri}, y_{iri} (the sequence of table cells).
If there are multiple solutions, you can print any of them. It is guaranteed that at least one solution exists.
3 3 3
3 1 1 1 2 1 3
3 2 1 2 2 2 3
3 3 1 3 2 3 3
2 3 1
6 1 1 1 2 1 3 2 3 2 2 2 1
Picture for the first sample:
Picture for the second sample:
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