{"raw_statement":[{"iden":"problem statement","content":"Takahashi has $A$ apple seedlings, $B$ banana seedlings, and $C$ cherry seedlings. Seedlings of the same kind cannot be distinguished.  \nHe will plant these seedlings in his $N$ gardens so that all of the following conditions are satisfied.\n\n*   At least one seedling must be planted in every garden.\n*   It is not allowed to plant two or more seedlings of the same kind in the same garden.\n*   It is not necessary to plant all seedlings he has.\n\nHow many ways are there to plant seedlings to satisfy the conditions? Find the count modulo $998244353$.  \nTwo ways are distinguished when there is a garden with different sets of seedlings planted in these two ways."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 5 \\times 10^6$\n*   $0 \\leq A \\leq N$\n*   $0 \\leq B \\leq N$\n*   $0 \\leq C \\leq N$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $A$ $B$ $C$"},{"iden":"sample input 1","content":"2 2 1 1"},{"iden":"sample output 1","content":"21\n\nAs illustrated below, there are $21$ ways to plant seedlings to satisfy the conditions.  \n(The two frames arranged vertically are the gardens. $A, B, C$ stand for apple, banana, cherry, respectively.)\n![image](https://img.atcoder.jp/ghi/30cbec3c4cc587889e3c37933da06c3f.png)"},{"iden":"sample input 2","content":"2 0 0 0"},{"iden":"sample output 2","content":"0\n\nThere may be no way to plant seedlings to satisfy the conditions."},{"iden":"sample input 3","content":"2 0 2 2"},{"iden":"sample output 3","content":"9"},{"iden":"sample input 4","content":"100 12 34 56"},{"iden":"sample output 4","content":"769445780"},{"iden":"sample input 5","content":"5000000 2521993 2967363 3802088"},{"iden":"sample output 5","content":"264705492"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}