{"raw_statement":[{"iden":"problem statement","content":"Snuke is playing a puzzle game. In this game, you are given a rectangular board of dimensions $R × C$, filled with numbers. Each integer $i$ from $1$ through $N$ is written twice, at the coordinates $(x_{i,1},y_{i,1})$ and $(x_{i,2},y_{i,2})$.\nThe objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from $1$ through $N$. Here, the curves may not go outside the board or cross each other.\nDetermine whether this is possible."},{"iden":"constraints","content":"*   $1 ≤ R,C ≤ 10^8$\n*   $1 ≤ N ≤ 10^5$\n*   $0 ≤ x_{i,1},x_{i,2} ≤ R(1 ≤ i ≤ N)$\n*   $0 ≤ y_{i,1},y_{i,2} ≤ C(1 ≤ i ≤ N)$\n*   All given points are distinct.\n*   All input values are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$R$ $C$ $N$\n$x_{1,1}$ $y_{1,1}$ $x_{1,2}$ $y_{1,2}$\n:\n$x_{N,1}$ $y_{N,1}$ $x_{N,2}$ $y_{N,2}$"},{"iden":"sample input 1","content":"4 2 3\n0 1 3 1\n1 1 4 1\n2 0 2 2"},{"iden":"sample output 1","content":"YES\n\n![image](https://atcoder.jp/img/arc076/hogehogehoge.png)\nThe above figure shows a possible solution."},{"iden":"sample input 2","content":"2 2 4\n0 0 2 2\n2 0 0 1\n0 2 1 2\n1 1 2 1"},{"iden":"sample output 2","content":"NO"},{"iden":"sample input 3","content":"5 5 7\n0 0 2 4\n2 3 4 5\n3 5 5 2\n5 5 5 4\n0 3 5 1\n2 2 4 4\n0 5 4 1"},{"iden":"sample output 3","content":"YES"},{"iden":"sample input 4","content":"1 1 2\n0 0 1 1\n1 0 0 1"},{"iden":"sample output 4","content":"NO"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}