Problem:
Score : 500 points

Problem Statement

There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.

Takahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.

Process the following Q queries:

The tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.

Constraints

All values in input are integers.

2 \leq N \leq 300

0 \leq M \leq \frac{N(N-1)}{2}

1 \leq L \leq 10^9

1 \leq A_i, B_i \leq N

A_i \neq B_i

\left(A_i, B_i\right) \neq \left(A_j, B_j\right) (if i \neq j)

\left(A_i, B_i\right) \neq \left(B_j, A_j\right) (if i \neq j)

1 \leq C_i \leq 10^9

1 \leq Q \leq N\left(N-1\right)

1 \leq s_i, t_i \leq N

s_i \neq t_i

\left(s_i, t_i\right) \neq \left(s_j, t_j\right) (if i \neq j)

Input

Input is given from Standard Input in the following format:

N M L
A_1 B_1 C_1
:
A_M B_M C_M
Q
s_1 t_1
:
s_Q t_Q

Output

Print Q lines.

The i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.

Sample Input 1

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

Sample Output 1

0
1

To travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.

To travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.

Sample Input 2

4 0 1
1
2 1

Sample Output 2

-1

There may be no road at all.

Sample Input 3

5 4 4
1 2 2
2 3 2
3 4 3
4 5 2
20
2 1
3 1
4 1
5 1
1 2
3 2
4 2
5 2
1 3
2 3
4 3
5 3
1 4
2 4
3 4
5 4
1 5
2 5
3 5
4 5

Sample Output 3

0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
2
2
1
0

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

#region using
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;
#endregion

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var M = consoleReader.Int;
            L = consoleReader.Int;

            {
                var gb = new LengthGraphBuilder(N);
                for (int i = 0; i < M; i++)
                {
                    var a = consoleReader.Int - 1;
                    var b = consoleReader.Int - 1;
                    var c = consoleReader.Int;
                    if (c <= L)
                        gb.Add(a, b, c);
                }
                graph = gb.ToArray();
            }
            var lengthes = LengthGraphBuilder.WarshallFloyd(graph);
            {
                var gb = new LengthGraphBuilder(N);
                for (int from = 0; from < N; from++)
                    for (int to = from + 1; to < N; to++)
                        if (lengthes[from, to] <= L)
                            gb.Add(from, to, 1);
                countGraph = gb.ToArray();
            }
            var counts = LengthGraphBuilder.WarshallFloyd(countGraph);


            var Q = consoleReader.Int;
            return AllLines(consoleReader.Repeat(Q).Select(cr => counts[cr.Int - 1, cr.Int - 1] - 1).Select(i => i > N ? -1 : i));
        }

        int L;
        Next[][] graph;
        Next[][] countGraph;

        struct Next
        {
            public int to;
            public int length;
            public override string ToString() => $"to: {to} length:{length}";
        }
        class LengthGraphBuilder
        {
            public List<Next>[] lists;
            public LengthGraphBuilder(int count)
            {
                this.lists = new List<Next>[count];
                for (int i = 0; i < count; i++)
                    this.lists[i] = new List<Next>();
            }
            public LengthGraphBuilder(int count, ConsoleReader cr, int edgeCount) : this(count)
            {
                for (int i = 0; i < edgeCount; i++)
                    this.Add(cr.Int - 1, cr.Int - 1, cr.Int);
            }
            public void Add(int from, int to, int length)
            {
                this.lists[from].Add(new Next { to = to, length = length });
                this.lists[to].Add(new Next { to = from, length = length }); // 有向の場合は消す
            }
            public Next[][] ToArray()
            {
                var N = this.lists.Length;
                var res = new Next[N][];
                for (int i = 0; i < N; i++)
                    res[i] = this.lists[i].ToArray();
                return res;
            }
            public static long[,] WarshallFloyd(Next[][] graph)
            {
                var res = new long[graph.Length, graph.Length];
                for (int i = 0; i < graph.Length; i++)
                {
                    for (int j = 0; j < graph.Length; j++)
                    {
                        res[i, j] = long.MaxValue / 2;
                    }
                    res[i, i] = 0;
                    foreach (var next in graph[i])
                        res[i, next.to] = next.length;
                }
                for (int k = 0; k < graph.Length; k++)
                    for (int i = 0; i < graph.Length; i++)
                        for (int j = 0; j < graph.Length; j++)
                            if (res[i, j] > res[i, k] + res[k, j])
                                res[i, j] = res[i, k] + res[k, j];
                return res;
            }
            public static long[] Dijkstra(Next[][] graph, int start)
            {
                var res = new long[graph.Length];
                for (int i = 0; i < res.Length; i++)
                    res[i] = int.MaxValue;
                res[start] = 0;
                var remains = new HashSet<int>(Enumerable.Range(0, graph.Length));
                while (remains.Count > 0)
                {
                    int minIndex = -1;
                    long min = long.MaxValue / 2;
                    foreach (var r in remains)
                    {
                        if (min > res[r])
                        {
                            minIndex = r;
                            min = res[r];
                        }
                    }
                    remains.Remove(minIndex);
                    foreach (var next in graph[minIndex])
                    {
                        var nextLength = min + next.length;
                        if (res[next.to] > nextLength)
                            res[next.to] = nextLength;
                    }
                }
                return res;
            }
        }


        #region いつもの
#pragma warning disable
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    #endregion
}