{"problem":{"name":"Counting of Trees","description":{"content":"Given is an integer sequence $D_1,...,D_N$ of $N$ elements. Find the number, modulo $998244353$, of trees with $N$ vertices numbered $1$ to $N$ that satisfy the following condition: *   For every int","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"nikkei2019_2_qual_b"},"statements":[{"statement_type":"Markdown","content":"Given is an integer sequence $D_1,...,D_N$ of $N$ elements. Find the number, modulo $998244353$, of trees with $N$ vertices numbered $1$ to $N$ that satisfy the following condition:\n\n*   For every integer $i$ from $1$ to $N$, the distance between Vertex $1$ and Vertex $i$ is $D_i$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $0 \\leq D_i \\leq N-1$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$D_1$ $D_2$ $...$ $D_N$\n\n[samples]\n\n## Notes\n\n*   A tree of $N$ vertices is a connected undirected graph with $N$ vertices and $N-1$ edges, and the distance between two vertices are the number of edges in the shortest path between them.\n*   Two trees are considered different if and only if there are two vertices $x$ and $y$ such that there is an edge between $x$ and $y$ in one of those trees and not in the other.","is_translate":false,"language":"English"}],"meta":{"iden":"nikkei2019_2_qual_b","tags":[],"sample_group":[["4\n0 1 1 2","2\n\nFor example, a tree with edges $(1,2)$, $(1,3)$, and $(2,4)$ satisfies the condition."],["4\n1 1 1 1","0"],["7\n0 3 2 1 2 2 1","24"]],"created_at":"2026-03-03 11:01:13"}}