Problem:
Score : 600 points

Problem Statement

We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N.

Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order of his choice.

The cost of using the string S_i once is C_i, and the cost of using it multiple times is C_i multiplied by that number of times.

Find the minimum total cost needed to choose strings so that Takahashi can make a palindrome.

If there is no choice of strings in which he can make a palindrome, print -1.

Constraints

1 \leq N \leq 50

1 \leq |S_i| \leq 20

S_i consists of lowercase English letters.

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
S_1 C_1
S_2 C_2
:
S_N C_N

Output

Print the minimum total cost needed to choose strings so that Takahashi can make a palindrome, or -1 if there is no such choice.

Sample Input 1

3
ba 3
abc 4
cbaa 5

Sample Output 1

7

We have ba, abc, and cbaa.

For example, we can use ba once and abc once for a cost of 7, then concatenate them in the order abc, ba to make a palindrome.
Also, we can use abc once and cbaa once for a cost of 9, then concatenate them in the order cbaa, abc to make a palindrome.

We cannot make a palindrome for a cost less than 7, so we should print 7.

Sample Input 2

2
abcab 5
cba 3

Sample Output 2

11

We can choose abcab once and cba twice, then concatenate them in the order abcab, cba, cba to make a palindrome for a cost of 11.

Sample Input 3

4
ab 5
cba 3
a 12
ab 10

Sample Output 3

8

We can choose a once, which is already a palindrome, but it is cheaper to concatenate ab and cba.

Sample Input 4

2
abc 1
ab 2

Sample Output 4

-1

We cannot make a palindrome, so we should print -1.

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

#region いつもの
using AtCoderProject;
using System;
using System.Collections.Generic;
using System.Linq;
using static AtCoderProject.Global;
using BigInteger = System.Numerics.BigInteger;
using BitOperations = System.Numerics.BitOperations;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using StringBuilder = System.Text.StringBuilder;
using Unsafe = System.Runtime.CompilerServices.Unsafe;

namespace AtCoderProject { using System.IO; using System.Text; using System.Diagnostics; using System.Runtime.CompilerServices; using System.Linq.Expressions; public static class Global { public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value); public static T[] NewArray<T>(int len0, Func<T> factory) { var arr = new T[len0]; for (int i = 0; i < arr.Length; i++) arr[i] = factory(); return arr; } public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value); return arr; } public static T[][] NewArray<T>(int len0, int len1, Func<T> factory) { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory) { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory) { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory); return arr; } public static long Pow(long x, int y) { long res = 1; for (; y > 0; y >>= 1) { if ((y & 1) == 1) res *= x; x *= x; } return res; } public static BigInteger ParseBigInteger(ReadOnlySpan<char> s) { /* 自前実装の方が速い */ BigInteger res; if (s.Length % 9 == 0) res = 0; else { res = new BigInteger(int.Parse(s.Slice(0, s.Length % 9))); s = s.Slice(s.Length % 9); } while (s.Length > 0) { var sp = s.Slice(0, 9); res *= 1000_000_000; res += int.Parse(sp); s = s.Slice(9); } return res; } public static int PopCount(int x) => BitOperations.PopCount((uint)x); public static int PopCount(long x) => BitOperations.PopCount((ulong)x); public static int PopCount(ulong x) => BitOperations.PopCount(x); public static int MSB(int x) => BitOperations.Log2((uint)x); public static int MSB(uint x) => BitOperations.Log2(x); public static int MSB(long x) => BitOperations.Log2((ulong)x); public static int MSB(ulong x) => BitOperations.Log2(x); public static int LSB(int x) => BitOperations.TrailingZeroCount((uint)x); public static int LSB(uint x) => BitOperations.TrailingZeroCount(x); public static int LSB(long x) => BitOperations.TrailingZeroCount((ulong)x); public static int LSB(ulong x) => BitOperations.TrailingZeroCount(x); } public static class Ext { public static bool UpdateMax<T>(this ref T r, T val) where T : struct, IComparable<T> { if (r.CompareTo(val) < 0) { r = val; return true; } return false; } public static bool UpdateMin<T>(this ref T r, T val) where T : struct, IComparable<T> { if (r.CompareTo(val) > 0) { r = val; return true; } return false; } public static long ToLong(this int i) => i; public static T[] Fill<T>(this T[] arr, T value) { Array.Fill(arr, value); return arr; } public static T[] Sort<T>(this T[] arr) { Array.Sort(arr); return arr; } public static string[] Sort(this string[] arr) => Sort(arr, StringComparer.OrdinalIgnoreCase); public static T[] Sort<T, U>(this T[] arr, Expression<Func<T, U>> selector) where U : IComparable<U> => Sort(arr, ExComparer<T>.CreateExp(selector)); public static T[] Sort<T>(this T[] arr, Comparison<T> comparison) { Array.Sort(arr, comparison); return arr; } public static T[] Sort<T>(this T[] arr, IComparer<T> comparer) { Array.Sort(arr, comparer); return arr; } public static T[] Reverse<T>(this T[] arr) { Array.Reverse(arr); return arr; } public static (int index, T max) MaxBy<T>(this T[] arr) where T : IComparable<T> { T max = arr[0]; int maxIndex = 0; for (int i = 0; i < arr.Length; i++) { if (max.CompareTo(arr[i]) < 0) { max = arr[i]; maxIndex = i; } } return (maxIndex, max); } public static (TSource item, TMax max) MaxBy<TSource, TMax>(this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector) where TMax : IComparable<TMax> { TMax max; TSource maxByItem; var e = source.GetEnumerator(); e.MoveNext(); maxByItem = e.Current; max = maxBySelector(maxByItem); while (e.MoveNext()) { var item = e.Current; var next = maxBySelector(item); if (max.CompareTo(next) < 0) { max = next; maxByItem = item; } } return (maxByItem, max); } public static (int index, T min) MinBy<T>(this T[] arr) where T : IComparable<T> { T min = arr[0]; int minIndex = 0; for (int i = 0; i < arr.Length; i++) { if (min.CompareTo(arr[i]) > 0) { min = arr[i]; minIndex = i; } } return (minIndex, min); } public static (TSource item, TMin min) MinBy<TSource, TMin>(this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector) where TMin : IComparable<TMin> { TMin min; TSource minByItem; var e = source.GetEnumerator(); e.MoveNext(); minByItem = e.Current; min = minBySelector(minByItem); while (e.MoveNext()) { var item = e.Current; var next = minBySelector(item); if (min.CompareTo(next) > 0) { min = next; minByItem = item; } } return (minByItem, min); } public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x)); 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 static Span<T> AsSpan<T>(this List<T> list, int start = 0) => Unsafe.As<Tuple<T[]>>(list).Item1.AsSpan(start, list.Count); public static ref T Get<T>(this T[] arr, int index) { if (index < 0) return ref arr[arr.Length + index]; return ref arr[index]; } public static TValue Get<TKey, TValue>(this IDictionary<TKey, TValue> dic, TKey key) { dic.TryGetValue(key, out var v); return v; } public static TValue GetOrInit<TKey, TValue>(this IDictionary<TKey, TValue> dic, TKey key, TValue value) { if (dic.TryGetValue(key, out var v)) return v; return dic[key] = value; } } public static class ExComparer<T> { class ExpressionComparer<K> : IComparer<T> where K : IComparable<K> { private class ParameterReplaceVisitor : ExpressionVisitor { private readonly ParameterExpression from; private readonly ParameterExpression to; public ParameterReplaceVisitor(ParameterExpression from, ParameterExpression to) { this.from = from; this.to = to; } protected override Expression VisitParameter(ParameterExpression node) => node == from ? to : base.VisitParameter(node); } readonly Comparison<T> func; public ExpressionComparer(Expression<Func<T, K>> expression) { var paramA = expression.Parameters[0]; var paramB = Expression.Parameter(typeof(T)); var f2 = (Expression<Func<T, K>>)new ParameterReplaceVisitor(expression.Parameters[0], paramB).Visit(expression); var compExp = Expression.Lambda<Comparison<T>>(Expression.Call(expression.Body, typeof(K).GetMethod(nameof(IComparable<K>.CompareTo), new[] { typeof(K) }), f2.Body), paramA, paramB); this.func = compExp.Compile(); } public int Compare(T x, T y) => func(x, y); public override bool Equals(object obj) => obj is ExpressionComparer<K> c && this.func == c.func; public override int GetHashCode() => func.GetHashCode(); } class ReverseComparer : IComparer<T> { private static Comparer<T> orig = Comparer<T>.Default; public int Compare(T y, T x) => orig.Compare(x, y); public override bool Equals(object obj) => obj is ReverseComparer; public override int GetHashCode() => GetType().GetHashCode(); } public static IComparer<T> CreateExp<K>(Expression<Func<T, K>> expression) where K : IComparable<K> => new ExpressionComparer<K>(expression); public static IComparer<T> DefaultReverse => new ReverseComparer(); } public class ΔDebugView<T> { private IEnumerable<T> collection; public ΔDebugView(IEnumerable<T> collection) { this.collection = collection ?? throw new ArgumentNullException(nameof(collection)); }[DebuggerBrowsable(DebuggerBrowsableState.RootHidden)] public T[] Items => collection.ToArray(); }[DebuggerStepThrough] public class ConsoleReader { const int BufSize = 1 << 12; private readonly byte[] buffer = new byte[BufSize]; private readonly Stream input; private readonly Encoding encoding; private int pos = 0; private int len = 0; public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; } public ConsoleReader(Stream input) : this(input, Console.InputEncoding) { } private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } } public int Int { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { int res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public int Int0 => this.Int - 1; public long Long { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { long res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public long Long0 => this.Long - 1; public string String { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return this.encoding.GetString(sb.ToArray()); } } public string Ascii { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new StringBuilder(); while (buffer[pos] <= 32) MoveNext(); do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return sb.ToString(); } } public string Line { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13); return this.encoding.GetString(sb.ToArray()); } } public char Char { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { while (buffer[pos] <= 32) MoveNext(); char res = (char)buffer[pos]; MoveNext(); return res; } } public double Double => double.Parse(this.Ascii);[DebuggerStepThrough] public struct RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; } public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } } public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } } public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } } public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } } public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } } public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } } public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } } public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } } public static implicit operator int[](RepeatReader rr) => rr.Int; public static implicit operator long[](RepeatReader rr) => rr.Long; public static implicit operator double[](RepeatReader rr) => rr.Double; public static implicit operator string[](RepeatReader rr) => rr.Ascii; } public RepeatReader Repeat(int count) => new RepeatReader(this, count);[DebuggerStepThrough] public struct SplitReader { ConsoleReader cr; public SplitReader(ConsoleReader cr) { this.cr = cr; } public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public static implicit operator int[](SplitReader sr) => sr.Int; public static implicit operator long[](SplitReader sr) => sr.Long; public static implicit operator double[](SplitReader sr) => sr.Double; public static implicit operator string[](SplitReader sr) => sr.Ascii; } public SplitReader Split => new SplitReader(this); public static implicit operator int(ConsoleReader cr) => cr.Int; public static implicit operator long(ConsoleReader cr) => cr.Long; public static implicit operator double(ConsoleReader cr) => cr.Double; public static implicit operator string(ConsoleReader cr) => cr.Ascii; public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2) => (o1, o2) = (this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3) => (o1, o2, o3) = (this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4) => (o1, o2, o3, o4) = (this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5) => (o1, o2, o3, o4, o5) = (this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6) => (o1, o2, o3, o4, o5, o6) = (this, this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6, out ConsoleReader o7) => (o1, o2, o3, o4, o5, o6, o7) = (this, this, this, this, this, this, this); public void Deconstruct(out ConsoleReader o1, out ConsoleReader o2, out ConsoleReader o3, out ConsoleReader o4, out ConsoleReader o5, out ConsoleReader o6, out ConsoleReader o7, out ConsoleReader o8) => (o1, o2, o3, o4, o5, o6, o7, o8) = (this, this, this, this, this, this, this, this); }[DebuggerStepThrough] public class ConsoleWriter {[DebuggerBrowsable(DebuggerBrowsableState.Never)] public readonly StreamWriter sw; public ConsoleWriter(Stream output) : this(output, Console.OutputEncoding) { } public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); } public void Flush() => sw.Flush(); public ConsoleWriter WriteLine(ReadOnlySpan<char> obj) { sw.WriteLine(obj); return this; } public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; } public ConsoleWriter WriteLineJoin<T>(ReadOnlySpan<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLines<T>(ReadOnlySpan<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols) { var en = cols.GetEnumerator(); while (en.MoveNext()) WriteLineJoin(en.Current); return this; } private ConsoleWriter WriteMany<T>(char sep, ReadOnlySpan<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } } }
public partial class Program {[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleReader cr;[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleWriter cw; public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; } static void Main() => new Program(new ConsoleReader(Console.OpenStandardInput()), new ConsoleWriter(Console.OpenStandardOutput())).Run(); public void Run() { var res = Calc(); if (res is double) cw.WriteLine(Result((double)res)); else if (res is bool) cw.WriteLine(Result((bool)res)); else if (res != null) cw.WriteLine(res.ToString()); cw.Flush(); } }
public partial class Program
{
    public static string Result(double d) => d.ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture);
    #endregion
    public static string Result(bool b) => b ? "Yes" : "No";
    private object Calc()
    {
        N = cr;
        SC = cr.Repeat(N).Select<(string S, int C)>(cr => (cr, cr));
        trie = new Trie<char, long>();
        foreach (var (s, c) in SC) trie.Add(s.AsSpan(), c);

        long res = INF;
        foreach (var (s, c) in SC)
        {
            var span = s.Append('a').ToArray().AsSpan();
            span.Reverse();
            res.UpdateMin(Calc(span.Slice(2)) + c);
            res.UpdateMin(Calc(span.Slice(1)) + c);
            for (char cc = 'a'; cc <= 'z'; cc++)
            {
                span[0] = cc;
                res.UpdateMin(Calc(span) + c);
            }
        }

        if (res >= INF) res = -1;
        return res;
    }

    long Calc(ReadOnlySpan<char> span)
    {
        if (span.Length == 0) return 0;
        var lists = NewArray(span.Length, () => new List<(int to, long v)>());
        for (int l = 0; l < span.Length; l++)
            for (int r = l + 1; r <= span.Length; r++)
            {
                var v = trie.Find(span[l..r]);
                if (v > 0)
                {
                    lists[l].Add((r, v));
                }
            }
        var costs = NewArray(span.Length, INF);
        for (int i = span.Length - 1; i >= 0; i--)
        {
            foreach (var (to, v) in lists[i].AsSpan())
            {
                if (to == span.Length)
                {
                    costs[i].UpdateMin(v);
                }
                else
                {
                    costs[i].UpdateMin(v + costs[to]);
                }
            }
        }

        return costs[0];
    }
    const long INF = long.MaxValue / 2000;
    int N;
    Trie<char, long> trie;
    (string S, int C)[] SC;
}

class Trie<TKey, TValue> { public Trie() : this(EqualityComparer<TKey>.Default) { } public Trie(IEqualityComparer<TKey> comparer) { this.comparer = comparer; this.children = new Dictionary<TKey, Trie<TKey, TValue>>(comparer); } private readonly IEqualityComparer<TKey> comparer; private readonly Dictionary<TKey, Trie<TKey, TValue>> children; public TValue Value { set; get; } public Trie<TKey, TValue> GetChild(IEnumerable<TKey> key) => GetChild(key, false); public Trie<TKey, TValue> GetChild(ReadOnlySpan<TKey> key) => GetChild(key, false); private Trie<TKey, TValue> GetChild(IEnumerable<TKey> key, bool force) { Trie<TKey, TValue> trie = this; foreach (var k in key) { if (!trie.children.TryGetValue(k, out var child)) { if (!force) return null; child = trie.children[k] = new Trie<TKey, TValue>(comparer); } trie = child; } return trie; } private Trie<TKey, TValue> GetChild(ReadOnlySpan<TKey> key, bool force) { Trie<TKey, TValue> trie = this; foreach (var k in key) { if (!trie.children.TryGetValue(k, out var child)) { if (!force) return null; child = trie.children[k] = new Trie<TKey, TValue>(comparer); } trie = child; } return trie; } public void Add(IEnumerable<TKey> key, TValue value) => GetChild(key, true).Value = value; public void Add(ReadOnlySpan<TKey> key, TValue value) => GetChild(key, true).Value = value; public TValue Find(IEnumerable<TKey> key) => GetChild(key, false) switch { { } child => child.Value, _ => default }; public TValue Find(ReadOnlySpan<TKey> key) => GetChild(key, false) switch { { } child => child.Value, _ => default }; }
class Trie<T> : Trie<T, bool> { public Trie() : base() { } public Trie(IEqualityComparer<T> comparer) : base(comparer) { } public void Add(IEnumerable<T> key) => Add(key, true); public void Add(ReadOnlySpan<T> key) => Add(key, true); }