{"raw_statement":[{"iden":"problem statement","content":"We have a grid with $A$ horizontal rows and $B$ vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:\n\n*   Assume that the grid currently has $a$ horizontal rows and $b$ vertical columns. Choose \"vertical\" or \"horizontal\".\n    *   If we choose \"vertical\", insert one row at the top of the grid, resulting in an $(a+1) \\times b$ grid.\n    *   If we choose \"horizontal\", insert one column at the right end of the grid, resulting in an $a \\times (b+1)$ grid.\n*   Then, paint one of the added squares black, and the other squares white.\n\nAssume the grid eventually has $C$ horizontal rows and $D$ vertical columns. Find the number of ways in which the squares can be painted in the end, modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq A \\leq C \\leq 3000$\n*   $1 \\leq B \\leq D \\leq 3000$\n*   $A$, $B$, $C$, and $D$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$A$ $B$ $C$ $D$"},{"iden":"sample input 1","content":"1 1 2 2"},{"iden":"sample output 1","content":"3\n\nAny two of the three squares other than the bottom-left square can be painted black."},{"iden":"sample input 2","content":"2 1 3 4"},{"iden":"sample output 2","content":"65"},{"iden":"sample input 3","content":"31 41 59 265"},{"iden":"sample output 3","content":"387222020"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}