{"problem":{"name":"Hop Sugoroku","description":{"content":"There is a row of $N$ squares labeled $1,2,\\dots,N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.   Initially, square $1$ is painted black, the other $N-1$ squares are painted white, and a pie","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2500,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc335_f"},"statements":[{"statement_type":"Markdown","content":"There is a row of $N$ squares labeled $1,2,\\dots,N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.  \nInitially, square $1$ is painted black, the other $N-1$ squares are painted white, and a piece is placed on square $1$.\nYou may repeat the following operation any number of times, possibly zero:\n\n*   When the piece is on square $i$, choose a positive integer $x$ and move the piece to square $i + A_i \\times x$.\n    *   Here, you cannot make a move with $i + A_i \\times x > N$.\n*   Then, paint the square $i + A_i \\times x$ black.\n\nFind the number of possible sets of squares that can be painted black at the end of the operations, modulo $998244353$.\n\n## Constraints\n\n*   All input values are integers.\n*   $1 \\le N \\le 2 \\times 10^5$\n*   $1 \\le A_i \\le 2 \\times 10^5$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\dots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc335_f","tags":[],"sample_group":[["5\n1 2 3 1 1","8\n\nThere are eight possible sets of squares painted black:\n\n*   Square $1$\n*   Squares $1,2$\n*   Squares $1,2,4$\n*   Squares $1,2,4,5$\n*   Squares $1,3$\n*   Squares $1,4$\n*   Squares $1,4,5$\n*   Squares $1,5$"],["1\n200000","1"],["40\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1","721419738\n\nBe sure to find the number modulo $998244353$."]],"created_at":"2026-03-03 11:01:13"}}