{"problem":{"name":"Infinite Sequence","description":{"content":"How many infinite sequences $a_1, a_2, ...$ consisting of {${1, ... ,n}$} satisfy the following conditions? *   The $n$\\-th and subsequent elements are all equal. That is, if $n \\leq i,j$, $a_i = a_j","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc071_d"},"statements":[{"statement_type":"Markdown","content":"How many infinite sequences $a_1, a_2, ...$ consisting of {${1, ... ,n}$} satisfy the following conditions?\n\n*   The $n$\\-th and subsequent elements are all equal. That is, if $n \\leq i,j$, $a_i = a_j$.\n*   For every integer $i$, the $a_i$ elements immediately following the $i$\\-th element are all equal. That is, if $i < j < k\\leq i+a_i$, $a_j = a_k$.\n\nFind the count modulo $10^9+7$.\n\n## Constraints\n\n*   $1 \\leq n \\leq 10^6$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$n$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc071_d","tags":[],"sample_group":[["2","4\n\nThe four sequences that satisfy the conditions are:\n\n*   $1, 1, 1, ...$\n*   $1, 2, 2, ...$\n*   $2, 1, 1, ...$\n*   $2, 2, 2, ...$"],["654321","968545283"]],"created_at":"2026-03-03 11:01:14"}}