Contest Duration: - (local time) (100 minutes) Back to Home
F - Figures /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• N-1 個の接続用部品が全て部品の接続に使われている。
• 部品を頂点とし、 接続用部品で接続された部品に対応する頂点組に辺が存在する N 頂点 N-1 辺の無向グラフを考えた際に、このグラフは連結である。

2 つの完成形について、全ての穴の組についてその 2 つを接続する接続用部品が存在するか否かが一致するとき、2 つの完成形が同じであると見なします。

### 制約

• 入力は全て整数
• 2 \leq N \leq 2 \times 10^5
• 1 \leq d_i < 998244353

### 入力

N
d_1 d_2 \cdots d_N


### 入力例 1

3
1 1 3


### 出力例 1

6


### 入力例 2

3
1 1 1


### 出力例 2

0


### 入力例 3

6
7 3 5 10 6 4


### 出力例 3

389183858


### 入力例 4

9
425656 453453 4320 1231 9582 54336 31435436 14342 423543


### 出力例 4

667877982


Score : 800 points

### Problem Statement

Takahashi is about to assemble a character figure, consisting of N parts called Part 1, Part 2, ..., Part N and N-1 connecting components. Parts are distinguishable, but connecting components are not.

Part i has d_i holes, called Hole 1, Hole 2, ..., Hole d_i, into which a connecting component can be inserted. These holes in the parts are distinguishable. Each connecting component will be inserted into two holes in different parts, connecting these two parts. It is impossible to insert multiple connecting components into a hole.

The character figure is said to be complete when it has the following properties:

• All of the N-1 components are used to connect parts.
• Consider a graph with N vertices corresponding to the parts and N-1 undirected edges corresponding to the pairs of vertices connected by a connecting component. Then, this graph is connected.

Two ways A and B to make the figure complete are considered the same when the following is satisfied: for every pair of holes, A uses a connecting component to connect these holes if and only if B uses one to connect them.

Find the number of ways to make the figure complete. Since the answer can be enormous, find the count modulo 998244353.

### Constraints

• All values in input are integers.
• 2 \leq N \leq 2 \times 10^5
• 1 \leq d_i < 998244353

### Input

Input is given from Standard Input in the following format:

N
d_1 d_2 \cdots d_N


### Sample Input 1

3
1 1 3


### Sample Output 1

6


One way to make the figure complete is to connect Hole 1 in Part 1 and Hole 3 in Part 3 and then connect Hole 1 in Part 2 and Hole 1 in Part 3.

### Sample Input 2

3
1 1 1


### Sample Output 2

0


### Sample Input 3

6
7 3 5 10 6 4


### Sample Output 3

389183858


### Sample Input 4

9
425656 453453 4320 1231 9582 54336 31435436 14342 423543


### Sample Output 4

667877982