Tiling

AtCoder

IDabc345_d

Time2000ms

Memory256MB

Difficulty—

There is a grid of $H$ rows and $W$ columns, each cell having a side length of $1$, and we have $N$ tiles. The $i$\-th tile ($1\leq i\leq N$) is a rectangle of size $A_i\times B_i$. Determine whether it is possible to place the tiles on the grid so that all of the following conditions are satisfied: * Every cell is covered by exactly one tile. * It is fine to have unused tiles. * The tiles **may be rotated or flipped when placed**. However, each tile must be aligned with the edges of the cells without extending outside the grid. ## Constraints * $1\leq N\leq 7$ * $1 \leq H,W \leq 10$ * $1\leq A_i,B_i\leq 10$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $H$ $W$ $A_1$ $B_1$ $A_2$ $B_2$ $\ldots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

Yes

Placing the $2$\-nd, $4$\-th, and $5$\-th tiles as shown below covers every cell of the grid by exactly one tile.
![image](https://img.atcoder.jp/abc345/0a0f2829d0485013deabba0103dbd906.png)
Hence, print `Yes`.

Input #2

1 1 2
2 3

Output #2

No

It is impossible to place the tile without letting it extend outside the grid.  
Hence, print `No`.

Input #3

1 2 2
1 1

Output #3

No

It is impossible to cover all cells with the tile.  
Hence, print `No`.

Input #4

Output #4

No

Note that each cell must be covered by exactly one tile.

API Response (JSON)

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      "content": "There is a grid of $H$ rows and $W$ columns, each cell having a side length of $1$, and we have $N$ tiles.  \nThe $i$\\-th tile ($1\\leq i\\leq N$) is a rectangle of size $A_i\\times B_i$.  \nDetermine whet...",
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