Problem:
Score : 1500 points

Problem Statement

You are given a tree with N vertices numbered 1, 2, ..., N. The i-th edge connects Vertex a_i and Vertex b_i.
You are also given a string S of length N consisting of 0 and 1. The i-th character of S represents the number of pieces placed on Vertex i.

Snuke will perform the following operation some number of times:

Choose two pieces the distance between which is at least 2, and bring these pieces closer to each other by 1. More formally, choose two vertices u and v, 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 u to its adjacent vertex on the path, and move one piece from v 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

2 \leq N \leq 2000

|S| = N

S consists of 0 and 1, and contains at least one 1.

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:

N
S
a_1 b_1
a_2 b_2
:
a_{N - 1} b_{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.

Sample Input 1

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

Sample Output 1

3

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

Choose the pieces on Vertex 3 and 5.

Choose the pieces on Vertex 2 and 7.

Choose the pieces on Vertex 4 and 6.

Sample Input 2

7
0010110
1 2
2 3
1 4
4 5
1 6
6 7

Sample Output 2

-1

Sample Input 3

2
01
1 2

Sample Output 3

0

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;


struct Myon2
{
    int a;
}

class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }

    Scanner cin;


    List<int>[] es;
    int N;
    string S;
    int[] parent;


    void calc()
    {
        cin = new Scanner();
        N = cin.nextInt();
        S = cin.next();
        es = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            es[i] = new List<int>();
        }

        for (int i = 0; i < N - 1; i++)
        {
            int a = cin.nextInt() - 1;
            int b = cin.nextInt() - 1;
            es[a].Add(b);
            es[b].Add(a);
        }

        int MAX = int.MaxValue / 2;
        ans = MAX;


        for (int i = 0; i < N; i++)
        {

            childCoin = new int[N];
            childSumLen = new long[N];
            childMinLen = new long[N];
            childMaxID = new int[N];
            parent = new int[N];

            dfs(i, -1);
            if (childMinLen[i] == 0)
            {

                ans = Math.Min(ans, childSumLen[i] / 2);
            }
        }

        if (ans == MAX) ans = -1;
        Console.WriteLine(ans);
    }

    int[] childCoin;
    long[] childSumLen;
    long[] childMinLen;
    int[] childMaxID;


    long ans;



    void dfs(int now, int pre)
    {
        parent[now] = pre;
        foreach (var next in es[now])
        {
            if (next == parent[now]) continue;
            dfs(next, now);
        }

        int maxID = -1;
        long maxMinLen = 0;


        foreach (var next in es[now])
        {
            if (next == parent[now]) continue;

            childCoin[now] += childCoin[next];
            childSumLen[now] += childSumLen[next] + childCoin[next];
            if (maxID == -1 || maxMinLen < childMinLen[next] + childCoin[next])
            {
                maxID = next;
                maxMinLen = childMinLen[next] + childCoin[next];
            }
        }
        childMaxID[now] = maxID;

        childMinLen[now] = maxMinLen;

        foreach (var next in es[now])
        {
            if (next == parent[now]) continue;
            if (next == maxID) continue;
            childMinLen[now] -= childSumLen[next] + childCoin[next];
        }

        childMinLen[now] = Math.Max(childMinLen[now], childSumLen[now] % 2);

        if (S[now] == '1') childCoin[now]++;

        //Console.WriteLine($"{now} {childCoin[now]} {childMinLen[now]} {childSumLen[now]}");
    }

}




class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}