CF441C.Valera and Tubes

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:

• r ≥ 2;
• for any integer i (1 ≤ i ≤ r - 1) the following equation |x__i - x__i + 1| + |y__i - y__i + 1| = 1 holds;
• each table cell, which belongs to the tube, must occur exactly once in the sequence.

Valera thinks that the tubes are arranged in a fancy manner if the following conditions are fulfilled:

• no pair of tubes has common cells;
• each cell of the table belongs to some tube.

Help Valera to arrange k tubes on his rectangle table in a fancy manner.

瓦列拉有一张由 $n$ 行 $m$ 列组成的矩形表格。瓦列拉将表格的行从上到下编号为 $1$ 至 $n$，列从左到右编号为 $1$ 至 $m$。我们将位于第 $x$ 行、第 $y$ 列的单元格表示为整数对 $(x,\,y)$。

瓦列拉希望在该矩形表格上恰好放置 $k$ 根“管子”（tube）。一根管子是如下形式的一串表格单元格：$(x_1,\,y_1),\ (x_2,\,y_2),\ \dots,\ (x_r,\,y_r)$，满足：

• $r \geq 2$；
• 对任意整数 $i$（$1 \leq i \leq r-1$），均满足 $|x_i - x_{i+1}| + |y_i - y_{i+1}| = 1$；
• 管子所经过的每个表格单元格在该序列中恰好出现一次。

瓦列拉认为，当且仅当满足以下条件时，这些管子的排布方式是“精巧的”（fancy）：

• 任意两根管子没有公共单元格；
• 表格中的每个单元格都属于且仅属于某一根管子。

请帮助瓦列拉在他的 $n \times m$ 矩形表格上以“精巧的方式”安排 $k$ 根管子。

The first line contains three space-separated integers n, m, k (2 ≤ n, m ≤ 300; 2 ≤ 2_k_ ≤ n·m) — the number of rows, the number of columns and the number of tubes, correspondingly.

第一行包含三个以空格分隔的整数 $n$、$m$、$k$（$2 \le n, m \le 300$；$2 \le 2k \le n\cdot m$），分别表示行数、列数和管子的数量。

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 2_r__i_ integers _x__i_1, _y__i_1, _x__i_2, _y__i_2, ..., x__ir__i, y__ir__i (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.

输出 k 行。在第 i 行中，输出第 i 个管子的描述：首先输出整数 r__i（该管子所占格子数），然后输出 2_r__i_ 个整数 _x__i_1, _y__i_1, _x__i_2, _y__i_2, ..., x__ir__i, y__ir__i（即该管子所覆盖的表格格子坐标序列）。

若存在多种解，输出任意一种即可。题目保证至少存在一个解。

Picture for the first sample:

Picture for the second sample:

第一个样例的图片：

第二个样例的图片：