using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;
using E = System.Linq.Enumerable;
using Weight = System.Int64;
using System.Threading;
internal partial class Solver {
public void Run() {
var n = ni();
var m = ni();
var D = new PrimalDual(n);
for (int i = 0; i < m; i++) {
var u = ni() - 1;
var v = ni() - 1;
var c = ni();
var d = ni();
D.AddEdge(u, v, 1, c);
D.AddEdge(u, v, 1, d);
D.AddEdge(v, u, 1, c);
D.AddEdge(v, u, 1, d);
}
cout.WriteLine(D.Run(0, n - 1, 2).TotalCost);
}
}
public class MinCostFlowResult {
public Weight TotalCost;
public Weight TotalFlow;
}
///
/// Cost can be negative.
/// O(FVE)
///
public class PrimalDual {
private readonly int N;
private readonly List> adjacents;
private readonly Weight[] _distance;
private readonly bool[] _inQueue;
private readonly Edge[] _prevEdges;
private readonly Queue _queue;
public class Edge {
public int From, To;
public Weight Flow, Capacity, Cost;
public Edge Reverse;
public Edge(int from, int to, Weight capacity, Weight cost, Weight flow = 0) {
From = from;
To = to;
Cost = cost;
Flow = flow;
Capacity = capacity;
}
public Weight Residue {
get {
return Capacity - Flow;
}
}
}
public PrimalDual(int n) {
N = n;
adjacents = new List>();
for (int i = 0; i < n; i++) {
adjacents.Add(new List());
}
_distance = new Weight[N];
_inQueue = new bool[N];
_prevEdges = new Edge[N];
_queue = new Queue(N);
}
public IEnumerable GetEdges() {
return adjacents.SelectMany(a => a);
}
public void AddEdge(int from, int to, Weight capacity, Weight cost) {
var e = new Edge(from, to, capacity, cost);
adjacents[from].Add(e);
}
private Edge[] FindShortestPathTree(int source) {
Array.Clear(_inQueue, 0, _inQueue.Length);
Array.Clear(_prevEdges, 0, _prevEdges.Length);
for (int i = 0; i < N; i++) {
_distance[i] = Weight.MaxValue;
}
_distance[source] = 0;
_inQueue[source] = true;
_queue.Enqueue(source);
while (_queue.Count > 0) { // SPFA
int now = _queue.Dequeue();
_inQueue[now] = false;
foreach (var e in adjacents[now]) {
if (e.Residue <= 0) {
continue;
}
if (_distance[now] != Weight.MaxValue && _distance[e.To] > _distance[now] + e.Cost) {
_distance[e.To] = _distance[now] + e.Cost;
_prevEdges[e.To] = e;
if (!_inQueue[e.To]) {
_inQueue[e.To] = true;
_queue.Enqueue(e.To);
}
}
}
}
return _prevEdges;
}
public MinCostFlowResult Run(int source, int sink, Weight flow) {
Weight totalCost = 0;
Weight totalFlow = 0;
while (totalFlow < flow) {
var prevEdges = FindShortestPathTree(source);
if (prevEdges[sink] == null) {
break;
}
long incrementalFlow = flow - totalFlow;
for (var e = prevEdges[sink]; e != null; e = prevEdges[e.From]) {
incrementalFlow = Math.Min(incrementalFlow, e.Residue);
}
for (var e = prevEdges[sink]; e != null; e = prevEdges[e.From]) {
if (e.Reverse == null) {
var reverseEdge = new Edge(e.To, e.From, 0, -e.Cost) {
Reverse = e
};
e.Reverse = reverseEdge;
adjacents[e.To].Add(reverseEdge);
}
totalCost += e.Cost * incrementalFlow;
e.Flow += incrementalFlow;
e.Reverse.Flow -= incrementalFlow;
}
totalFlow += incrementalFlow;
}
return new MinCostFlowResult { TotalCost = totalCost, TotalFlow = totalFlow };
}
}
// PREWRITEN CODE BEGINS FROM HERE
static public class StringExtensions {
static public string JoinToString(this IEnumerable source, string separator = " ") {
return string.Join(separator, source);
}
}
internal partial class Solver : Scanner {
static readonly int? StackSizeInMebiByte = null; //50;
public static void StartAndJoin(Action action, int maxStackSize) {
var thread = new Thread(new ThreadStart(action), maxStackSize);
thread.Start();
thread.Join();
}
public static void Main() {
#if LOCAL
byte[] inputBuffer = new byte[1000000];
var inputStream = Console.OpenStandardInput(inputBuffer.Length);
using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
Console.SetIn(reader);
new Solver(Console.In, Console.Out).Run();
}
#else
Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
if (StackSizeInMebiByte.HasValue) {
StartAndJoin(() => new Solver(Console.In, Console.Out).Run(), StackSizeInMebiByte.Value * 1024 * 1024);
} else {
new Solver(Console.In, Console.Out).Run();
}
Console.Out.Flush();
#endif
}
#pragma warning disable IDE0052
private readonly TextReader cin;
private readonly TextWriter cout;
private readonly TextWriter cerr;
#pragma warning restore IDE0052
public Solver(TextReader reader, TextWriter writer)
: base(reader) {
cin = reader;
cout = writer;
cerr = Console.Error;
}
public Solver(string input, TextWriter writer)
: this(new StringReader(input), writer) {
}
#pragma warning disable IDE1006
#pragma warning disable IDE0051
private int ni() { return NextInt(); }
private int[] ni(int n) { return NextIntArray(n); }
private long nl() { return NextLong(); }
private long[] nl(int n) { return NextLongArray(n); }
private double nd() { return NextDouble(); }
private double[] nd(int n) { return NextDoubleArray(n); }
private string ns() { return Next(); }
private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}
#if DEBUG
internal static class LinqPadExtension {
public static string TextDump(this T obj) {
if (obj is IEnumerable) return (obj as IEnumerable).Cast