{"problem":{"name":"FG operation","description":{"content":"We have a sequence of $N$ integers between $0$ and $9$ (inclusive): $A=(A_1, \\dots, A_N)$, arranged from left to right in this order. Until the length of the sequence becomes $1$, we will repeatedly d","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc220_d"},"statements":[{"statement_type":"Markdown","content":"We have a sequence of $N$ integers between $0$ and $9$ (inclusive): $A=(A_1, \\dots, A_N)$, arranged from left to right in this order.\nUntil the length of the sequence becomes $1$, we will repeatedly do the operation $F$ or $G$ below.\n\n*   Operation $F$: delete the leftmost two values (let us call them $x$ and $y$) and then insert $(x+y)\\%10$ to the left end.\n*   Operation $G$: delete the leftmost two values (let us call them $x$ and $y$) and then insert $(x\\times y)\\%10$ to the left end.\n\nHere, $a\\%b$ denotes the remainder when $a$ is divided by $b$.\nFor each $K=0,1,\\dots,9$, answer the following question.\n\n> Among the $2^{N-1}$ possible ways in which we do the operations, how many end up with $K$ being the final value of the sequence?  \n> Since the answer can be enormous, find it modulo $998244353$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^5$\n*   $0 \\leq A_i \\leq 9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $\\dots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc220_d","tags":[],"sample_group":[["3\n2 7 6","1\n0\n0\n0\n2\n1\n0\n0\n0\n0\n\nIf we do Operation $F$ first and Operation $F$ second: the sequence becomes $(2,7,6)→(9,6)→(5)$.  \nIf we do Operation $F$ first and Operation $G$ second: the sequence becomes $(2,7,6)→(9,6)→(4)$.  \nIf we do Operation $G$ first and Operation $F$ second: the sequence becomes $(2,7,6)→(4,6)→(0)$.  \nIf we do Operation $G$ first and Operation $G$ second: the sequence becomes $(2,7,6)→(4,6)→(4)$."],["5\n0 1 2 3 4","6\n0\n1\n1\n4\n0\n1\n1\n0\n2"]],"created_at":"2026-03-03 11:01:14"}}