CSU1811：Tree Intersection（树启发式合并）

Bobo has a tree with n vertices numbered by 1,2,…,n and (n-1) edges. The i-th vertex has color c  _i, and the i-th edge connects vertices a  _i and b  _i.

Let C(x,y) denotes the set of colors in subtree rooted at vertex x deleting edge (x,y).

Bobo would like to know R_i which is the size of intersection of C(a  _i,b  _i) and C(b _i,a  _i) for all 1≤i≤(n-1). (i.e. |C(a  _i,b  _i)∩C(b  _i,a  _i)|)

Input

The input contains at most 15 sets. For each set:

The first line contains an integer n (2≤n≤10  ⁵).

The second line contains n integers c  ₁,c  ₂,…,c  _n (1≤c_i≤n).

The i-th of the last (n-1) lines contains 2 integers a  _i,b  _i (1≤a  _i,b  _i≤n).

OutputFor each set, (n-1) integers R  ₁,R  ₂,…,R  _n-1.Sample Input

4
1 2 2 1
1 2
2 3
3 4
5
1 1 2 1 2
1 3
2 3
3 5
4 5

Sample Output

1
2
1
1
1
2
1

题意：给一棵树，每个点有一种颜色，问对于每一条边，删除这条边之后形成的两棵子树的相交颜色种数。

思路：启发式合并，维护每个子树的颜色及其数量，分别讨论颜色的“由无到有”和“由有到满”两种情况就行了。这题还能用莫队算法，留坑。

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