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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
namespace Program
{
    public static class ABC000A
    {
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var M = NN;
            var L = NN;
            var abcList = Repeat(0, M).Select(_ => new { A = NN - 1, B = NN - 1, C = NN }).ToArray();
            var Q = NN;
            var queryList = Repeat(0, Q).Select(_ => new { s = NN - 1, t = NN - 1 }).ToArray();
            var path = Repeat(0, N).Select(_ => new List<Tuple<long, long>>()).ToArray();
            foreach (var abc in abcList)
            {
                path[abc.A].Add(Tuple.Create(abc.B, abc.C));
                path[abc.B].Add(Tuple.Create(abc.A, abc.C));
            }
            var ans = new long[N, N];
            for (var i = 0; i < N; i++)
            {
                {
                    var dist = Repeat(1000000000000000000, N).ToArray();
                    var enery = Repeat(0L, N).ToArray();
                    var q = new RadixHeap<long>();
                    dist[i] = 0;
                    enery[i] = L;
                    q.Push(0, i);
                    var status = new bool[N];
                    status[i] = true;
                    while (q.Count > 0)
                    {
                        var t = q.Pop();
                        var v = t.Item2;
                        if (!status[v]) continue;
                        status[v] = false;
                        foreach (var item in path[v])
                        {
                            var eneTemp = 0L;
                            var distTemp = 0L;
                            if (enery[v] < item.Item2)
                            {
                                if (L < item.Item2)
                                {
                                    continue;
                                }
                                else
                                {
                                    eneTemp = L - item.Item2;
                                    distTemp = dist[v] + 1;
                                }
                            }
                            else
                            {
                                eneTemp = enery[v] - item.Item2;
                                distTemp = dist[v];
                            }
                            if (dist[item.Item1] > distTemp ||
                               (dist[item.Item1] == distTemp && enery[item.Item1] < eneTemp))
                            {
                                enery[item.Item1] = eneTemp;
                                dist[item.Item1] = distTemp;
                                q.Push(dist[item.Item1] * L + (L - enery[item.Item1]), item.Item1);
                                status[item.Item1] = true;
                            }
                        }
                    }
                    for (var j = 0; j < N; j++)
                    {
                        if (dist[j] > 1000000000000000)
                        {
                            ans[i, j] = -1;
                        }
                        else
                        {
                            ans[i, j] = dist[j];
                        }
                    }
                }
            }
            for (var i = 0; i < Q; i++)
            {
                Console.WriteLine(ans[queryList[i].s, queryList[i].t]);

            }
        }
        static public void Main(string[] args) { if (args.Length == 0) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); } var t = new Thread(Solve, 134217728); t.Start(); t.Join(); Console.Out.Flush(); }
        static class Console_
        {
            static Queue<string> param = new Queue<string>();
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => xorshift);
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IEnumerable<long> Primes(long x) { if (x < 2) yield break; yield return 2; var halfx = x / 2; var table = new bool[halfx + 1]; var max = (long)(Math.Sqrt(x) / 2); for (long i = 1; i <= max; ++i) { if (table[i]) continue; var add = 2 * i + 1; yield return add; for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true; } for (long i = max + 1; i <= halfx; ++i) if (!table[i] && 2 * i + 1 <= x) yield return 2 * i + 1; }
        static IEnumerable<long> Factors(long x) { if (x < 2) yield break; while (x % 2 == 0) { x /= 2; yield return 2; } var max = (long)Math.Sqrt(x); for (long i = 3; i <= max; i += 2) while (x % i == 0) { x /= i; yield return i; } if (x != 1) yield return x; }
        static IEnumerable<long> Divisor(long x) { if (x < 1) yield break; var max = (long)Math.Sqrt(x); for (long i = 1; i <= max; ++i) { if (x % i != 0) continue; yield return i; if (i != x / i) yield return x / i; } }
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
        static long GCD(long a, long b) { while (b > 0) { var tmp = b; b = a % b; a = tmp; } return a; }
        static long LCM(long a, long b) => a * b / GCD(a, b);
        static Mod Pow(Mod x, long y) { Mod a = 1; while (y != 0) { if ((y & 1) == 1) a.Mul(x); x.Mul(x); y >>= 1; } return a; }
        static long Pow(long x, long y) { long a = 1; while (y != 0) { if ((y & 1) == 1) a *= x; x *= x; y >>= 1; } return a; }
        static List<long> _fact = new List<long>() { 1 };
        static void _B(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
        static long Comb(long n, long k) { _B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
        static long Perm(long n, long k) { _B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)]; }
        static Func<TR> Lambda<TR>(Func<Func<TR>, TR> f) { Func<TR> t = () => default(TR); return t = () => f(t); }
        static Func<T1, TR> Lambda<T1, TR>(Func<T1, Func<T1, TR>, TR> f) { Func<T1, TR> t = x1 => default(TR); return t = x1 => f(x1, t); }
        static Func<T1, T2, TR> Lambda<T1, T2, TR>(Func<T1, T2, Func<T1, T2, TR>, TR> f) { Func<T1, T2, TR> t = (x1, x2) => default(TR); return t = (x1, x2) => f(x1, x2, t); }
        static Func<T1, T2, T3, TR> Lambda<T1, T2, T3, TR>(Func<T1, T2, T3, Func<T1, T2, T3, TR>, TR> f) { Func<T1, T2, T3, TR> t = (x1, x2, x3) => default(TR); return t = (x1, x2, x3) => f(x1, x2, x3, t); }
        static Func<T1, T2, T3, T4, TR> Lambda<T1, T2, T3, T4, TR>(Func<T1, T2, T3, T4, Func<T1, T2, T3, T4, TR>, TR> f) { Func<T1, T2, T3, T4, TR> t = (x1, x2, x3, x4) => default(TR); return t = (x1, x2, x3, x4) => f(x1, x2, x3, x4, t); }
        static List<T> LCS<T>(T[] s, T[] t) where T : IEquatable<T> { int sl = s.Length, tl = t.Length; var dp = new int[sl + 1, tl + 1]; for (var i = 0; i < sl; i++) for (var j = 0; j < tl; j++) dp[i + 1, j + 1] = s[i].Equals(t[j]) ? dp[i, j] + 1 : Max(dp[i + 1, j], dp[i, j + 1]); { var r = new List<T>(); int i = sl, j = tl; while (i > 0 && j > 0) if (s[--i].Equals(t[--j])) r.Add(s[i]); else if (dp[i, j + 1] > dp[i + 1, j]) ++j; else ++i; r.Reverse(); return r; } }
        static long LIS<T>(T[] array, bool strict) { var l = new List<T>(); foreach (var e in array) { var i = l.BinarySearch(e); if (i < 0) i = ~i; else if (!strict) ++i; if (i == l.Count) l.Add(e); else l[i] = e; } return l.Count; }
        class PQ<T>
        {
            List<T> h; Comparison<T> c; public T Peek => h[0]; public int Count => h.Count;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, Comparer<T>.Default.Compare, asc) { }
            public PQ(bool asc = true) : this(Comparer<T>.Default.Compare, asc) { }
            public void Push(T v) { var i = h.Count; h.Add(v); while (i > 0) { var ni = (i - 1) / 2; if (c(v, h[ni]) >= 0) break; h[i] = h[ni]; i = ni; } h[i] = v; }
            public T Pop() { var r = h[0]; var v = h[h.Count - 1]; h.RemoveAt(h.Count - 1); if (h.Count == 0) return r; var i = 0; while (i * 2 + 1 < h.Count) { var i1 = i * 2 + 1; var i2 = i * 2 + 2; if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2; if (c(v, h[i1]) <= 0) break; h[i] = h[i1]; i = i1; } h[i] = v; return r; }
        }
        class PQ<TK, TV>
        {
            PQ<Tuple<TK, TV>> q; public Tuple<TK, TV> Peek => q.Peek; public int Count => q.Count;
            public PQ(int cap, Comparison<TK> c, bool asc = true) { q = new PQ<Tuple<TK, TV>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TK> c, bool asc = true) { q = new PQ<Tuple<TK, TV>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, Comparer<TK>.Default.Compare, asc) { }
            public PQ(bool asc = true) : this(Comparer<TK>.Default.Compare, asc) { }
            public void Push(TK k, TV v) => q.Push(Tuple.Create(k, v));
            public Tuple<TK, TV> Pop() => q.Pop();
        }
        public class UF
        {
            long[] d;
            public UF(long s) { d = Repeat(-1L, s).ToArray(); }
            public bool Unite(long x, long y) { x = Root(x); y = Root(y); if (x != y) { if (d[y] < d[x]) { var t = y; y = x; x = t; } d[x] += d[y]; d[y] = x; } return x != y; }
            public bool IsSame(long x, long y) => Root(x) == Root(y);
            public long Root(long x) => d[x] < 0 ? x : d[x] = Root(d[x]);
            public long Count(long x) => -d[Root(x)];
        }
        struct Mod : IEquatable<Mod>, IEquatable<long>
        {
            static public long _mod = 1000000007; long v;
            public Mod(long x) { if (x < _mod && x >= 0) v = x; else if ((v = x % _mod) < 0) v += _mod; }
            static public implicit operator Mod(long x) => new Mod(x);
            static public implicit operator long(Mod x) => x.v;
            public void Add(Mod x) { if ((v += x.v) >= _mod) v -= _mod; }
            public void Sub(Mod x) { if ((v -= x.v) < 0) v += _mod; }
            public void Mul(Mod x) => v = (v * x.v) % _mod;
            public void Div(Mod x) => v = (v * Inverse(x.v)) % _mod;
            static public Mod operator +(Mod x, Mod y) { var t = x.v + y.v; return t >= _mod ? new Mod { v = t - _mod } : new Mod { v = t }; }
            static public Mod operator -(Mod x, Mod y) { var t = x.v - y.v; return t < 0 ? new Mod { v = t + _mod } : new Mod { v = t }; }
            static public Mod operator *(Mod x, Mod y) => x.v * y.v;
            static public Mod operator /(Mod x, Mod y) => x.v * Inverse(y.v);
            static public bool operator ==(Mod x, Mod y) => x.v == y.v;
            static public bool operator !=(Mod x, Mod y) => x.v != y.v;
            static public long Inverse(long x) { long b = _mod, r = 1, u = 0, t = 0; while (b > 0) { var q = x / b; t = u; u = r - q * u; r = t; t = b; b = x - q * b; x = t; } return r < 0 ? r + _mod : r; }
            public bool Equals(Mod x) => v == x.v;
            public bool Equals(long x) => v == x;
            public override bool Equals(object x) => x == null ? false : Equals((Mod)x);
            public override int GetHashCode() => v.GetHashCode();
            public override string ToString() => v.ToString();
            static List<Mod> _fact = new List<Mod>() { 1 };
            static void B(long n) { if (n >= _fact.Count) for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i); }
            static public Mod Comb(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k]; }
            static public Mod Perm(long n, long k) { B(n); if (n == 0 && k == 0) return 1; if (n < k || n < 0) return 0; return _fact[(int)n] / _fact[(int)(n - k)]; }
        }
        class Tree
        {
            long N; int l; List<long>[] p; int[] d; long[][] pr; long r; Tuple<long, long, int>[] e; Tuple<long, long>[] b; bool lca; bool euler; bool bfs;
            public Tree(List<long>[] p_, long r_) { N = p_.Length; p = p_; r = r_; lca = false; euler = false; }
            public Tuple<long, long>[] BFSRoot() { if (!bfs) { var nb = new List<Tuple<long, long>>(); var q = new Queue<long>(); var d = new bool[N]; nb.Add(Tuple.Create(r, -1L)); d[r] = true; q.Enqueue(r); while (q.Count > 0) { var w = q.Dequeue(); foreach (var i in p[w]) { if (d[i]) continue; d[i] = true; q.Enqueue(i); nb.Add(Tuple.Create(i, w)); } } b = nb.ToArray(); bfs = true; } return b; }
            public Tuple<long, long>[] BFSLeaf() => BFSRoot().Reverse().ToArray();
            public Tuple<long, long, int>[] Euler() { if (!euler) { var ne = new List<Tuple<long, long, int>>(); var s = new Stack<Tuple<long, long>>(); var d = new bool[N]; d[r] = true; s.Push(Tuple.Create(r, -1L)); while (s.Count > 0) { var w = s.Peek(); var ad = true; foreach (var i in p[w.Item1]) { if (d[i]) continue; d[i] = true; ad = false; s.Push(Tuple.Create(i, w.Item1)); } if (!ad || p[w.Item1].Count == 1) ne.Add(Tuple.Create(w.Item1, w.Item2, 1)); if (ad) { s.Pop(); ne.Add(Tuple.Create(w.Item1, w.Item2, -1)); } } e = ne.ToArray(); euler = true; } return e; }
            public long LCA(long u, long v) { if (!lca) { l = 0; while (N > (1 << l)) l++; d = new int[N]; pr = Repeat(0, l).Select(_ => new long[N]).ToArray(); d[r] = 0; pr[0][r] = -1; var q = new Stack<long>(); q.Push(r); while (q.Count > 0) { var w = q.Pop(); foreach (var i in p[w]) { if (i == pr[0][w]) continue; q.Push(i); d[i] = d[w] + 1; pr[0][i] = w; } } for (var k = 0; k + 1 < l; k++) for (var w = 0; w < N; w++) if (pr[k][w] < 0) pr[k + 1][w] = -1; else pr[k + 1][w] = pr[k][pr[k][w]]; lca = true; } if (d[u] > d[v]) { var t = u; u = v; v = t; } for (var k = 0; k < l; k++) if ((((d[v] - d[u]) >> k) & 1) != 0) v = pr[k][v]; if (u == v) return u; for (var k = l - 1; k >= 0; k--) if (pr[k][u] != pr[k][v]) { u = pr[k][u]; v = pr[k][v]; } return pr[0][u]; }
        }
        class BT<T> where T : IComparable
        {
            class Node { public Node l; public Node r; public T v; public bool b; public int c; }
            Comparison<T> c; Node r; bool ch; T lm;
            public BT(Comparison<T> _c) { c = _c; }
            public BT() : this((x, y) => x.CompareTo(y)) { }
            bool R(Node n) => n != null && !n.b;
            bool B(Node n) => n != null && n.b;
            long C(Node n) => n?.c ?? 0;
            Node RtL(Node n) { Node m = n.r, t = m.l; m.l = n; n.r = t; n.c -= m.c - (t?.c ?? 0); m.c += n.c - (t?.c ?? 0); return m; }
            Node RtR(Node n) { Node m = n.l, t = m.r; m.r = n; n.l = t; n.c -= m.c - (t?.c ?? 0); m.c += n.c - (t?.c ?? 0); return m; }
            Node RtLR(Node n) { n.l = RtL(n.l); return RtR(n); }
            Node RtRL(Node n) { n.r = RtR(n.r); return RtL(n); }
            public void Add(T x) { r = A(r, x); r.b = true; }
            Node A(Node n, T x) { if (n == null) { ch = true; return new Node() { v = x, c = 1 }; } if (c(x, n.v) < 0) n.l = A(n.l, x); else n.r = A(n.r, x); n.c++; return Bl(n); }
            Node Bl(Node n) { if (!ch) return n; if (!B(n)) return n; if (R(n.l) && R(n.l.l)) { n = RtR(n); n.l.b = true; } else if (R(n.l) && R(n.l.r)) { n = RtLR(n); n.l.b = true; } else if (R(n.r) && R(n.r.l)) { n = RtRL(n); n.r.b = true; } else if (R(n.r) && R(n.r.r)) { n = RtL(n); n.r.b = true; } else ch = false; return n; }
            public void Remove(T x) { r = Rm(r, x); if (r != null) r.b = true; }
            Node Rm(Node n, T x) { if (n == null) { ch = false; return n; } n.c--; var r = c(x, n.v); if (r < 0) { n.l = Rm(n.l, x); return BlL(n); } if (r > 0) { n.r = Rm(n.r, x); return BlR(n); } if (n.l == null) { ch = n.b; return n.r; } n.l = RmM(n.l); n.v = lm; return BlL(n); }
            Node RmM(Node n) { n.c--; if (n.r != null) { n.r = RmM(n.r); return BlR(n); } lm = n.v; ch = n.b; return n.l; }
            Node BlL(Node n) { if (!ch) return n; if (B(n.r) && R(n.r.l)) { var b = n.b; n = RtRL(n); n.b = b; n.l.b = true; ch = false; } else if (B(n.r) && R(n.r.r)) { var b = n.b; n = RtL(n); n.b = b; n.r.b = true; n.l.b = true; ch = false; } else if (B(n.r)) { ch = n.b; n.b = true; n.r.b = false; } else { n = RtL(n); n.b = true; n.l.b = false; n.l = BlL(n.l); ch = false; } return n; }
            Node BlR(Node n) { if (!ch) return n; if (B(n.l) && R(n.l.r)) { var b = n.b; n = RtLR(n); n.b = b; n.r.b = true; ch = false; } else if (B(n.l) && R(n.l.l)) { var b = n.b; n = RtR(n); n.b = b; n.l.b = true; n.r.b = true; ch = false; } else if (B(n.l)) { ch = n.b; n.b = true; n.l.b = false; } else { n = RtR(n); n.b = true; n.r.b = false; n.r = BlR(n.r); ch = false; } return n; }
            public T this[long i] { get { return At(r, i); } }
            T At(Node n, long i) { if (n == null) return default(T); if (n.l == null) if (i == 0) return n.v; else return At(n.r, i - 1); if (n.l.c == i) return n.v; if (n.l.c > i) return At(n.l, i); return At(n.r, i - n.l.c - 1); }
            public bool Have(T x) { var t = FindUpper(x); return t < C(r) && c(At(r, t), x) == 0; }
            public long FindUpper(T x, bool allowSame = true) => allowSame ? FL(r, x) + 1 : FU(r, x);
            long FU(Node n, T x) { if (n == null) return 0; var r = c(x, n.v); if (r < 0) return FU(n.l, x); return C(n.l) + 1 + FU(n.r, x); }
            public long FindLower(T x, bool allowSame = true) { var t = FL(r, x); if (allowSame) return t + 1 < C(r) && c(At(r, t + 1), x) == 0 ? t + 1 : t < 0 ? C(r) : t; return t < 0 ? C(r) : t; }
            long FL(Node n, T x) { if (n == null) return -1; var r = c(x, n.v); if (r > 0) return C(n.l) + 1 + FL(n.r, x); return FL(n.l, x); }
            public T Min() { Node n = r, p = null; while (n != null) { p = n; n = n.l; } return p == null ? default(T) : p.v; }
            public T Max() { Node n = r, p = null; while (n != null) { p = n; n = n.r; } return p == null ? default(T) : p.v; }
            public bool Any() => r != null;
            public long Count() => C(r);
            public IEnumerable<T> List() => L(r);
            IEnumerable<T> L(Node n) { if (n == null) yield break; foreach (var i in L(n.l)) yield return i; yield return n.v; foreach (var i in L(n.r)) yield return i; }
        }
        class Dict<K, V> : Dictionary<K, V>
        {
            Func<K, V> d;
            public Dict(Func<K, V> _d) { d = _d; }
            public Dict() : this(_ => default(V)) { }
            new public V this[K i] { get { V v; return TryGetValue(i, out v) ? v : base[i] = d(i); } set { base[i] = value; } }
        }
        class Deque<T>
        {
            T[] b; int o, c;
            public int Count;
            public T this[int i] { get { return b[gi(i)]; } set { b[gi(i)] = value; } }
            public Deque(int cap = 16) { b = new T[c = cap]; }
            int gi(int i) { if (i >= c) throw new Exception(); var r = o + i; return r >= c ? r - c : r; }
            public void PushFront(T x) { if (Count == c) e(); if (--o < 0) o += b.Length; b[o] = x; ++Count; }
            public T PopFront() { if (Count-- == 0) throw new Exception(); var r = b[o++]; if (o >= c) o -= c; return r; }
            public T Front => b[o];
            public void PushBack(T x) { if (Count == c) e(); var i = o + Count++; b[i >= c ? i - c : i] = x; }
            public T PopBack() { if (Count == 0) throw new Exception(); return b[gi(--Count)]; }
            public T Back => b[gi(Count - 1)];
            void e() { T[] nb = new T[c << 1]; if (o > c - Count) { var l = b.Length - o; Array.Copy(b, o, nb, 0, l); Array.Copy(b, 0, nb, l, Count - l); } else Array.Copy(b, o, nb, 0, Count); b = nb; o = 0; c <<= 1; }
            public void Insert(int i, T x) { if (i > Count) throw new Exception(); this.PushFront(x); for (int j = 0; j < i; j++) this[j] = this[j + 1]; this[i] = x; }
            public T RemoveAt(int i) { if (i < 0 || i >= Count) throw new Exception(); var r = this[i]; for (int j = i; j > 0; j--) this[j] = this[j - 1]; this.PopFront(); return r; }
        }
        class SegTree<T>
        {
            int n; T ti; Func<T, T, T> f; T[] dat;
            public SegTree(long _n, T _ti, Func<T, T, T> _f) { n = 1; while (n < _n) n <<= 1; ti = _ti; f = _f; dat = Repeat(ti, n << 1).ToArray(); for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public SegTree(List<T> l, T _ti, Func<T, T, T> _f) : this(l.Count, _ti, _f) { for (var i = 0; i < l.Count; i++) dat[n + i] = l[i]; for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public void Update(long i, T v) { dat[i += n] = v; while ((i >>= 1) > 0) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public T Query(long l, long r) { var vl = ti; var vr = ti; for (long li = n + l, ri = n + r; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) vl = f(vl, dat[li++]); if ((ri & 1) == 1) vr = f(dat[--ri], vr); } return f(vl, vr); }
            public T this[long idx] { get { return dat[idx + n]; } set { Update(idx, value); } }
        }
        class LazySegTree<T, E>
        {
            int n, height; T ti; E ei; Func<T, T, T> f; Func<T, E, T> g; Func<E, E, E> h; T[] dat; E[] laz;
            public LazySegTree(long _n, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, T> _g, Func<E, E, E> _h) { n = 1; height = 0; while (n < _n) { n <<= 1; ++height; } ti = _ti; ei = _ei; f = _f; g = _g; h = _h; dat = Repeat(ti, n << 1).ToArray(); laz = Repeat(ei, n << 1).ToArray(); for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            public LazySegTree(List<T> l, T _ti, E _ei, Func<T, T, T> _f, Func<T, E, T> _g, Func<E, E, E> _h) : this(l.Count, _ti, _ei, _f, _g, _h) { for (var i = 0; i < l.Count; i++) dat[n + i] = l[i]; for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); }
            T Reflect(long i) => laz[i].Equals(ei) ? dat[i] : g(dat[i], laz[i]);
            void Eval(long i) { if (laz[i].Equals(ei)) return; laz[(i << 1) | 0] = h(laz[(i << 1) | 0], laz[i]); laz[(i << 1) | 1] = h(laz[(i << 1) | 1], laz[i]); dat[i] = Reflect(i); laz[i] = ei; }
            void Thrust(long i) { for (var j = height; j > 0; j--) Eval(i >> j); }
            void Recalc(long i) { while ((i >>= 1) > 0) dat[i] = f(Reflect((i << 1) | 0), Reflect((i << 1) | 1)); }
            public void Update(long l, long r, E v) { Thrust(l += n); Thrust(r += n - 1); for (long li = l, ri = r + 1; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) { laz[li] = h(laz[li], v); ++li; } if ((ri & 1) == 1) { --ri; laz[ri] = h(laz[ri], v); } } Recalc(l); Recalc(r); }
            public T Query(long l, long r) { Thrust(l += n); Thrust(r += n - 1); var vl = ti; var vr = ti; for (long li = l, ri = r + 1; li < ri; li >>= 1, ri >>= 1) { if ((li & 1) == 1) vl = f(vl, Reflect(li++)); if ((ri & 1) == 1) vr = f(Reflect(--ri), vr); } return f(vl, vr); }
            public T this[long idx] { get { Thrust(idx += n); return dat[idx] = Reflect(idx); } set { Thrust(idx += n); dat[idx] = value; laz[idx] = ei; Recalc(idx); } }
        }
        class RadixHeap<T>
        {
            public int bsr(ulong x)
            {
                ulong l = 9223372036854775808;
                var idx = 63;
                while (l != 0 && (x & l) == 0)
                {
                    l >>= 1;
                    --idx;
                }
                return idx;
            }
            List<Tuple<ulong, T>>[] v;
            ulong last;
            ulong size;
            public int Count => (int)size;
            public RadixHeap()
            {
                v = Repeat(0, 65).Select(_ => new List<Tuple<ulong, T>>()).ToArray();
                last = size = 0;
            }
            public void Push(long x, T value)
            {
                ++size;
                ulong key = (ulong)x;
                v[bsr(key ^ last) + 1].Add(Tuple.Create(key, value));
            }
            public Tuple<ulong, T> Pop()
            {
                if (v[0].Count == 0)
                {
                    var i = 1;
                    while (v[i].Count == 0) ++i;
                    var newLast = v[i].Min(e2 => e2.Item1);
                    foreach (var item in v[i])
                    {
                        v[bsr(item.Item1 ^ newLast) + 1].Add(item);
                    }
                    last = newLast;
                    v[i].Clear();
                }
                --size;
                var ret = v[0].Last();
                v[0].RemoveAt(v[0].Count - 1);
                return ret;
            }
        }
    }
}