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E. Lomsat gelral

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.

Let's call colour *c* dominating in the subtree of vertex *v* if there are no other colours that appear in the subtree of vertex *v* more times than colour *c*. So it's possible that two or more colours will be dominating in the subtree of some vertex.

The subtree of vertex *v* is the vertex *v* and all other vertices that contains vertex *v* in each path to the root.

For each vertex *v* find the sum of all dominating colours in the subtree of vertex *v*.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of vertices in the tree.

The second line contains *n* integers *c*_{i} (1 ≤ *c*_{i} ≤ *n*), *c*_{i} — the colour of the *i*-th vertex.

Each of the next *n* - 1 lines contains two integers *x*_{j}, *y*_{j} (1 ≤ *x*_{j}, *y*_{j} ≤ *n*) — the edge of the tree. The first vertex is the root of the tree.

Output

Print *n* integers — the sums of dominating colours for each vertex.

Examples

Input

4

1 2 3 4

1 2

2 3

2 4

Output

10 9 3 4

Input

15

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

1 2

1 3

1 4

1 14

1 15

2 5

2 6

2 7

3 8

3 9

3 10

4 11

4 12

4 13

Output

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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