# 2021 年东华大学金马程序设计联赛

G. IDEA's Tree
PDF 题面可用

IDEA has a tree with $n(1\leq n\leq 5000)$ nodes. Now she select a connected subgraph on the tree randomly, please help her calculate the expected size of connected subgraph she select (module $998244353$).

### 输入格式

There are multiple test cases.

For each test case, in the first line, there is an integer n, denoting the node number of the tree.

Then for the next $n-1$ lines, $i$-th line contains an integer $u$, indicate that there is an edge between $i+1$ and $u$.

### 输出格式

For each test cases, print the answer in one line.

### 样例

Input
3
1
1

Output
665496237


NaN