Maxim is a big fan of various games. This time, he is playing a game called "Heroes of Might and Magic III".
Each scenario in the game is played on a specific map, which is a rectangle consisting of $$$n \times m$$$ cells. Each cell has its own type of terrain, such as "grass", "swamp", "sand", etc. Visually, some cells with the same type of terrain form connected components$$$^{\ast}$$$. There can be many such components, but Maxim prefers scenarios where the map has no more than two types of terrain and the total number of connected components is exactly $$$k$$$.
You, as the most experienced map maker, have promised to come up with a map that Maxim will like. Will you be able to keep this promise?
Connected component$$$^{\ast}$$$ – is a connected area of the table consisting of the same symbol, and for any pair of cells $$$(x_{1}, y_{1})$$$, $$$(x_{2}, y_{2})$$$ belonging to this area, there exists a path from $$$(x_{1}, y_{1})$$$ to $$$(x_{2}, y_{2})$$$$$$^{\ast}$$$, consisting only of cells from this connected area.
Path in the table from $$$(x_{1}, y_{1})$$$ to $$$(x_{2}, y_{2})$$$$$$^{\ast}$$$ – is a sequence of cells that starts at $$$(x_{1}, y_{1})$$$, ends at $$$(x_{2}, y_{2})$$$ and any two adjacent cells in this sequence are neighbors by side.
A single line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \le n, m \le 1000$$$, $$$1 \le k \le n \cdot m$$$).
If such a map can be created, then in the first line print "YES" without quotes and then print the map itself from a new line. It should consist of the symbols '0' and '1' and have exactly $$$k$$$ connected components.
If it is impossible to build such a map, then print "NO" without quotes.
5 5 5
YES 00001 11111 00000 01001 11101
3 3 6
YES 010 001 010
5 4 19
NO
4 4 11
YES 1010 0010 0101 1010
