问题 I: WO MEI K

There is a weighted tree with $n$ vertices and $n-1$ edges. each edge has a value. Let $f(v,u)$ be the number of values that appear exactly once on the edges of a simple path between vertices $v$ and $u$.

Now you randomly choose $k$ vertices, which is x1,x2,…,xk. For all $k=1,2,\dots ,n$, calculate the expectation of ek=∑i=1k∑j=i+1kf(xi,xj) modulo $998244353$

This problem contains multiple test cases.The first line of input contains a single integer $t(1\le t\le 2\cdot 10^5)$---the number of test cases.The description of test cases follows.

In a test, the first line contains a single integer $n$ ($2\le n\le 2\cdot 10^5$) --- the number of island

Each of the next $n-1$ lines contains three integers $v,u$ and $x$ ($1\le v,u,x\le n$) --- This means that this egde connects $u$ and $v$, and the value of this edge is $x$.

It's guarantee the sum of $n$ over all test cases doesn't exceed $10^6$.

2
2
1 2 1
3
1 2 1
1 3 2

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