[BZOJ3669][Noi2014]魔法森林

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <algorithm>
using namespace std;

int read() {
	int x = 0, f = 1; char c = getchar();
	while(!isdigit(c)){ if(c == ‘-‘) f = -1; c = getchar(); }
	while(isdigit(c)){ x = x * 10 + c - ‘0‘; c = getchar(); }
	return x * f;
}

#define maxn 50010
#define maxm 100010
#define maxnode 150010
#define oo 2147483647

struct Node {
	int a, b, mxa, mxb;
	bool rev;
	Node(): rev(0) {}
	Node(int _, int __): a(_), b(__) {}
} ns[maxnode];
int fa[maxnode], ch[maxnode][2], S[maxnode], top;
bool isrt(int u) { return !fa[u] || (ch[fa[u]][0] != u && ch[fa[u]][1] != u); }
void maintain(int o) {
	ns[o].mxa = ns[o].mxb = o;
	for(int i = 0; i < 2; i++) if(ch[o][i]) {
		int son = ns[ch[o][i]].mxa, &mea = ns[o].mxa;
		if(ns[son].a > ns[mea].a) mea = son;
		son = ns[ch[o][i]].mxb; int &meb = ns[o].mxb;
		if(ns[son].b > ns[meb].b) meb = son;
	}
	return ;
}
void pushdown(int o) {
	if(!ns[o].rev) return ;
	swap(ch[o][0], ch[o][1]);
	for(int i = 0; i < 2; i++) if(ch[o][i])
		ns[ch[o][i]].rev ^= 1;
	ns[o].rev = 0;
	return ;
}
void rotate(int u) {
	int y = fa[u], z = fa[y], l = 0, r = 1;
	if(!isrt(y)) ch[z][ch[z][1]==y] = u;
	if(ch[y][1] == u) swap(l, r);
	fa[u] = z; fa[y] = u; fa[ch[u][r]] = y;
	ch[y][l] = ch[u][r]; ch[u][r] = y;
	maintain(y); maintain(u);
	return ;
}
void splay(int u) {
	int t = u; S[top = 1] = t;
	while(!isrt(t)) S[++top] = fa[t], t = fa[t];
	while(top) pushdown(S[top--]);
	while(!isrt(u)) {
		int y = fa[u], z = fa[y];
		if(!isrt(y)) {
			if(ch[y][0] == u ^ ch[z][0] == y) rotate(u);
			else rotate(y);
		}
		rotate(u);
	}
	return ;
}
void access(int u) {
	splay(u); ch[u][1] = 0; maintain(u);
	while(fa[u]) splay(fa[u]), ch[fa[u]][1] = u, maintain(fa[u]), splay(u);
	return ;
}
void makeroot(int u) {
	access(u); ns[u].rev ^= 1;
	return ;
}
void link(int a, int b) {
	makeroot(b); fa[b] = a;
	return ;
}
void cut(int a, int b) {
	makeroot(a); access(b); ch[b][0] = fa[a] = 0; maintain(a);
	return ;
}
int _a, _b;
void query(int a, int b) {
	makeroot(a); access(b);
	_a = ns[b].mxa; _b = ns[b].mxb;
	return ;
}

struct Edge {
	int u, v, a, b;
	Edge() {}
	Edge(int _1, int _2, int _3, int _4): u(_1), v(_2), a(_3), b(_4) {}
	bool operator < (const Edge& t) const { return a < t.a; }
} es[maxm];

int pa[maxn];
int findset(int x) { return x == pa[x] ? x : pa[x] = findset(pa[x]); }

int ans;

int main() {
	int n = read(), m = read();
	for(int i = 1; i <= n; i++) ns[i] = Node(0, 0), maintain(i), pa[i] = i;
	for(int i = 1; i <= m; i++) {
		int u = read(), v = read(), a = read(), b = read();
		es[i] = Edge(u, v, a, b);
	}
	sort(es + 1, es + m + 1);
	
	ans = oo;
//	for(int i = 1; i <= m; i++) printf("Edge %d: %d %d %d %d\n", i, es[i].u, es[i].v, es[i].a, es[i].b);
	for(int i = 1; i <= m; i++) {
		int u = es[i].u, v = es[i].v, U = findset(u), V = findset(v);
		ns[i+n] = Node(es[i].a, es[i].b); maintain(i + n);
		if(U == V) {
			query(u, v);
			if(ns[_b].b > es[i].b) {
				cut(es[_b-n].u, _b); cut(_b, es[_b-n].v);
				link(u, i + n); link(i + n, v);
			}
		}
		else {
			pa[V] = U;
			link(u, i + n); link(i + n, v);
		}
		if(findset(1) == findset(n)) {
			query(1, n);
			ans = min(ans, ns[_a].a + ns[_b].b);
		}
	}
	
	printf("%d\n", ans < oo ? ans : -1);
	
	return 0;
}