{"raw_statement":[{"iden":"problem statement","content":"There are $N$ squares called Square $1$ though Square $N$. You start on Square $1$.\nEach of the squares from Square $1$ through Square $N-1$ has a die on it. The die on Square $i$ is labeled with the integers from $0$ through $A_i$, each occurring with equal probability. (Die rolls are independent of each other.)\nUntil you reach Square $N$, you will repeat rolling a die on the square you are on. Here, if the die on Square $x$ rolls the integer $y$, you go to Square $x+y$.\nFind the expected value, modulo $998244353$, of the number of times you roll a die."},{"iden":"notes","content":"It can be proved that the sought expected value is always a rational number. Additionally, if that value is represented $\\frac{P}{Q}$ using two coprime integers $P$ and $Q$, there is a unique integer $R$ such that $R \\times Q \\equiv P\\pmod{998244353}$ and $0 \\leq R \\lt 998244353$. Find this $R$."},{"iden":"constraints","content":"*   $2 \\le N \\le 2 \\times 10^5$\n*   $1 \\le A_i \\le N-i(1 \\le i \\le N-1)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\dots$ $A_{N-1}$"},{"iden":"sample input 1","content":"3\n1 1"},{"iden":"sample output 1","content":"4\n\nThe sought expected value is $4$, so $4$ should be printed.\nHere is one possible scenario until reaching Square $N$:\n\n*   Roll $1$ on Square $1$, and go to Square $2$.\n*   Roll $0$ on Square $2$, and stay there.\n*   Roll $1$ on Square $2$, and go to Square $3$.\n\nThis scenario occurs with probability $\\frac{1}{8}$."},{"iden":"sample input 2","content":"5\n3 1 2 1"},{"iden":"sample output 2","content":"332748122"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}