{"problem":{"name":"Gardens","description":{"content":"Takahashi has $A$ apple seedlings, $B$ banana seedlings, and $C$ cherry seedlings. Seedlings of the same kind cannot be distinguished.   He will plant these seedlings in his $N$ gardens so that all of","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc235_g"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq N \\leq 5 \\times 10^6$\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.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $A$ $B$ $C$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc235_g","tags":[],"sample_group":[["2 2 1 1","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)"],["2 0 0 0","0\n\nThere may be no way to plant seedlings to satisfy the conditions."],["2 0 2 2","9"],["100 12 34 56","769445780"],["5000000 2521993 2967363 3802088","264705492"]],"created_at":"2026-03-03 11:01:14"}}