atcoder#AGC034E. [AGC034E] Complete Compress

[AGC034E] Complete Compress

Score : 15001500 points

Problem Statement

You are given a tree with NN vertices numbered 1,2,...,N1, 2, ..., N. The ii-th edge connects Vertex aia_i and Vertex bib_i. You are also given a string SS of length NN consisting of 0 and 1. The ii-th character of SS represents the number of pieces placed on Vertex ii.

Snuke will perform the following operation some number of times:

  • Choose two pieces the distance between which is at least 22, and bring these pieces closer to each other by 11. More formally, choose two vertices uu and vv, each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from uu to its adjacent vertex on the path, and move one piece from vv to its adjacent vertex on the path.

By repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible? If the answer is yes, also find the minimum number of operations required to achieve it.

Constraints

  • 2N20002 \leq N \leq 2000
  • S=N|S| = N
  • SS consists of 0 and 1, and contains at least one 1.
  • 1ai,biN(aibi)1 \leq a_i, b_i \leq N(a_i \neq b_i)
  • The edges $(a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1})$ forms a tree.

Input

Input is given from Standard Input in the following format:

NN

SS

a1a_1 b1b_1

a2a_2 b2b_2

::

aN1a_{N - 1} bN1b_{N - 1}

Output

If it is impossible to have all the pieces on the same vertex, print -1. If it is possible, print the minimum number of operations required.

7
0010101
1 2
2 3
1 4
4 5
1 6
6 7
3

We can gather all the pieces in three operations as follows:

  • Choose the pieces on Vertex 33 and 55.
  • Choose the pieces on Vertex 22 and 77.
  • Choose the pieces on Vertex 44 and 66.
7
0010110
1 2
2 3
1 4
4 5
1 6
6 7
-1
2
01
1 2
0