Description:
You found a painting on a canvas of size $$$n \times m$$$. The canvas can be represented as a grid with $$$n$$$ rows and $$$m$$$ columns. Each cell has some color. Cell $$$(i, j)$$$ has color $$$c_{i,j}$$$.
Near the painting you also found a brush in the shape of a $$$2 \times 2$$$ square, so the canvas was surely painted in the following way: initially, no cell was painted. Then, the following painting operation has been performed some number of times:
- Choose two integers $$$i$$$ and $$$j$$$ ($$$1 \le i < n$$$, $$$1 \le j < m$$$) and some color $$$k$$$ ($$$1 \le k \le nm$$$).
- Paint cells $$$(i, j)$$$, $$$(i + 1, j)$$$, $$$(i, j + 1)$$$, $$$(i + 1, j + 1)$$$ in color $$$k$$$.
All cells must be painted at least once. A cell can be painted multiple times. In this case, its final color will be the last one.
Find any sequence of at most $$$nm$$$ operations that could have led to the painting you found or state that it's impossible.
Input Format:
The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n, m \le 1000$$$) — the dimensions of the canvas.
On the $$$i$$$-th of the next $$$n$$$ lines of input, there will be $$$m$$$ integers. The $$$j$$$-th of them is $$$a_{i,j}$$$ ($$$1 \le a_{i,j} \le nm$$$) — the color of cell $$$(i, j)$$$.
Output Format:
If there is no solution, print a single integer $$$-1$$$.
Otherwise, on the first line, print one integer $$$q$$$ ($$$1 \le q \le nm$$$) — the number of operations.
Next, print the operations in order. On the $$$k$$$-th of the next $$$q$$$ lines, print three integers $$$i$$$, $$$j$$$, $$$c$$$ ($$$1 \le i < n$$$, $$$1 \le j < m$$$, $$$1 \le c \le nm$$$) — the description of the $$$k$$$-th operation.
If there are multiple solutions, print any.
Note:
In the first test case, the solution is not unique. Here's one of them:
In the second test case, there is no way one could obtain the given painting, thus the answer is $$$-1$$$.