#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
using namespace std;
// Trash code from https://www.geeksforgeeks.org/pairing-heap/
struct HeapNode {
pair<int, int> key;
HeapNode *leftChild;
HeapNode *nextSibling;
HeapNode():
leftChild(NULL), nextSibling(NULL) {}
// creates a new node
HeapNode(pair<int, int> key_, HeapNode *leftChild_, HeapNode *nextSibling_):
key(key_), leftChild(leftChild_), nextSibling(nextSibling_) {}
// Adds a child and sibling to the node
void addChild(HeapNode *node) {
if(leftChild == NULL)
leftChild = node;
else {
node->nextSibling = leftChild;
leftChild = node;
}
}
};
// Returns true if root of the tree
// is null otherwise returns false
bool Empty(HeapNode *node) {
return (node == NULL);
}
// Function to merge two heaps
HeapNode *Merge(HeapNode *A, HeapNode *B)
{
// If any of the two-nodes is null
// the return the not null node
if(A == NULL) return B;
if(B == NULL) return A;
// To maintain the min heap condition compare
// the nodes and node with minimum value become
// parent of the other node
if(A->key < B->key) {
A->addChild(B);
return A;
}
else {
B->addChild(A);
return B;
}
return NULL; // Unreachable
}
// Returns the root value of the heap
pair<int, int> Top(HeapNode *node) {
return node->key;
}
// Function to insert the new node in the heap
HeapNode *Insert(HeapNode *node, pair<int, int> key) {
return Merge(node, new HeapNode(key, NULL, NULL));
}
// This method is used when we want to delete root node
HeapNode *TwoPassMerge(HeapNode *node) {
if(node == NULL || node->nextSibling == NULL)
return node;
else {
HeapNode *A, *B, *newNode;
A = node;
B = node->nextSibling;
newNode = node->nextSibling->nextSibling;
A->nextSibling = NULL;
B->nextSibling = NULL;
return Merge(Merge(A, B), TwoPassMerge(newNode));
}
return NULL; // Unreachable
}
// Function to delete the root node in heap
HeapNode *Delete(HeapNode *node) {
return TwoPassMerge(node->leftChild);
}
struct PairingHeap {
HeapNode *root;
PairingHeap():
root(NULL) {}
bool Empty(void) {
return ::Empty(root);
}
pair<int, int> Top(void) {
return ::Top(root);
}
void Insert(pair<int, int> key) {
root = ::Insert(root, key);
}
void Delete(void) {
root = ::Delete(root);
}
void Join(PairingHeap other) {
root = ::Merge(root, other.root);
}
};
struct edge {
int from, to, weight, cost, id;
edge() {}
edge(int _from, int _to, int _weight, int _cost, int _id) : from(_from), to(_to), weight(_weight), cost(_cost), id(_id) {}
};
struct node {
int distance, parent;
node() {
distance = INT_MAX;
parent = -1;
}
node(int _distance, int _parent) : distance(_distance), parent(_parent) {}
};
struct result {
int edge;
vector<int> distances;
};
vector<node> dijkstra(vector<vector<edge>> graph, int start) {
int n = (int)graph.size();
vector<node> answer(n);
PairingHeap q;
q.Insert({0, start});
answer[start].distance = 0;
while (!q.Empty()) {
auto [d, u] = q.Top();
q.Delete();
if (answer[u].distance > d) {
continue;
}
for (auto [from, to, weight, cost, id] : graph[u]) {
if (answer[from].distance + weight < answer[to].distance) {
answer[to] = node(answer[from].distance + weight, id);
q.Insert({answer[to].distance, to});
}
}
}
return answer;
}
vector<vector<edge>> transpose(vector<vector<edge>> graph) {
int n = (int)graph.size();
vector<vector<edge>> new_graph(n);
for (int u = 0; u < n; u++) {
for (auto [from, to, weight, cost, id] : graph[u]) {
new_graph[to].emplace_back(to, from, weight, cost, id);
}
}
return new_graph;
}
vector<vector<int>> find_shortest_paths_without_each_edge(vector<vector<edge>> graph, int start) {
int n = (int)graph.size();
int m = 0;
for (int u = 0; u < n; u++) {
for (auto [from, to, weight, cost, id] : graph[u]) {
m = max(m, 1 + id);
}
}
vector<node> result = dijkstra(graph, start);
vector<int> dist(n);
for (int i = 0; i < n; i++) {
dist[i] = result[i].distance;
}
vector<vector<int>> answer(m);
for (auto [distance, parent] : result) {
if (parent != -1) {
vector<vector<edge>> new_graph = graph;
for (int u = 0; u < n; u++) {
for (int i = 0; i < (int)new_graph[u].size(); i++) {
auto [from, to, weight, cost, id] = new_graph[u][i];
if (id == parent) {
new_graph[u].erase(new_graph[u].begin() + i);
break;
}
}
}
vector<node> new_result = dijkstra(new_graph, start);
answer[parent] = vector<int>(n);
for (int i = 0; i < n; i++) {
answer[parent][i] = new_result[i].distance;
}
}
}
answer.push_back(dist);
return answer;
}
void solve() {
int n, m;
cin >> n >> m;
vector<vector<edge>> graph(n);
for (int i = 0; i < m; i++) {
int from, to, weight, cost;
cin >> from >> to >> weight >> cost;
from--, to--;
graph[from].emplace_back(from, to, weight, cost, i);
}
vector<vector<edge>> rev_graph = transpose(graph);
vector<vector<int>> result_a = find_shortest_paths_without_each_edge(graph, 0);
vector<vector<int>> result_b = find_shortest_paths_without_each_edge(graph, n - 1);
vector<vector<int>> rev_result_a = find_shortest_paths_without_each_edge(rev_graph, 0);
vector<vector<int>> rev_result_b = find_shortest_paths_without_each_edge(rev_graph, n - 1);
auto get = [](vector<vector<int>>& x, int i, int j) {
if (x[i].empty()) {
return x.back()[j];
} else {
return x[i][j];
}
};
int ans = INT_MAX;
if (result_a.back()[n - 1] != INT_MAX && result_b.back()[0] != INT_MAX) {
ans = result_a.back()[n - 1] + result_b.back()[0];
}
for (int u = 0; u < n; u++) {
for (auto [from, to, weight, cost, id] : graph[u]) {
int AB = INT_MAX, BA = INT_MAX;
AB = min(AB, get(result_a, id, n - 1));
if (get(result_a, id, to) != INT_MAX && get(rev_result_b, id, from) != INT_MAX) {
AB = min(AB, get(result_a, id, to) + get(rev_result_b, id, from) + weight);
}
BA = min(BA, get(result_b, id, 0));
if (get(result_b, id, to) != INT_MAX && get(rev_result_a, id, from) != INT_MAX) {
BA = min(BA, get(result_b, id, to) + get(rev_result_a, id, from) + weight);
}
if (AB == INT_MAX || BA == INT_MAX) {
continue;
}
ans = min(ans, AB + BA + cost);
}
}
cout << (ans == INT_MAX ? -1 : ans) << "\n";
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
