Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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B. Apple Tree

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a rooted tree with *n* vertices. In each leaf vertex there's a single integer — the number of apples in this vertex.

The weight of a subtree is the sum of all numbers in this subtree leaves. For instance, the weight of a subtree that corresponds to some leaf is the number written in the leaf.

A tree is balanced if for every vertex *v* of the tree all its subtrees, corresponding to the children of vertex *v*, are of equal weight.

Count the minimum number of apples that you need to remove from the tree (specifically, from some of its leaves) in order to make the tree balanced. Notice that you can always achieve the goal by just removing all apples.

Input

The first line contains integer *n* (2 ≤ *n* ≤ 10^{5}), showing the number of vertices in the tree. The next line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 10^{8}), *a*_{i} is the number of apples in the vertex number *i*. The number of apples in non-leaf vertices is guaranteed to be zero.

Then follow *n* - 1 lines, describing the tree edges. Each line contains a pair of integers *x*_{i}, *y*_{i} (1 ≤ *x*_{i}, *y*_{i} ≤ *n*, *x*_{i} ≠ *y*_{i}) — the vertices connected by an edge.

The vertices are indexed from 1 to *n*. Vertex 1 is the root.

Output

Print a single integer — the minimum number of apples to remove in order to make the tree balanced.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the sin, cout streams cin, cout or the %I64d specifier.

Examples

Input

6

0 0 12 13 5 6

1 2

1 3

1 4

2 5

2 6

Output

6

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