迷途知返 - Problem

#7374. 迷途知返

Statistics

The problem was used in the following contests:

Elegia's Forgotten Hill

This problem is prepared by Elegia .

题目描述

有一条 $n+1$ 个点的链，设其从一端到另一端的编号依次为 $0,1,\dots,n$。忆艾想知道有多少条从 $0$ 出发，又回到原点的欧拉回路，满足：经过 $(i-1,i)$ 这条边的次数恰为 $2d_i$。你只需要输出答案对 $998244353$ 取模的结果。

输入格式

第一行输入一个正整数 $n$。

接下来一行输入 $n$ 个正整数，第 $i$ 个为 $d_i$。

输出格式

输出一个整数表示方案数同余 $998244353$。

样例 1

输入

2
2 1

输出

解释

走一步后，可以选择继续前进或者折返，再往后都只有唯一选择。

样例 2

输入

4
200 30 8 11

输出

812059605

数据范围

对于 $100\%$ 的数据，保证 $1\le n,d_i\le 10^5$。

时间限制 $1\,\mathrm{s}$，空间限制 $512\,\mathrm{MB}$。

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