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| #include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define sqz main
#define ll long long
#define rep(i, a, b) for (int i = (a); i <= (b); i++)
#define per(i, a, b) for (int i = (a); i >= (b); i--)
#define Rep(i, a, b) for (int i = (a); i < (b); i++)
#define travel(i, u) for (int i = head[u]; ~i; i = edge[i].next)
const ll INF = 1e9, Mo = 998244353;
const int N = 50000, M = 100000;
const double eps = 1e-6;
namespace slow_IO
{
ll read()
{
ll x = 0; int zf = 1; char ch = getchar();
while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
if (ch == '-') zf = -1, ch = getchar();
while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
return x * zf;
}
void write(ll y)
{
if (y < 0) putchar('-'), y = -y;
if (y > 9) write(y / 10);
putchar(y % 10 + '0');
}
}
using namespace slow_IO;
struct node
{
int u, v, a, b;
node() {}
node(int _u, int _v, int _a, int _b) {u = _u, v = _v, a = _a, b = _b;}
}Edge[M + 5];
inline int cmp(node X, node Y)
{
return X.a < Y.a;
}
struct LinkCutTree
{
int Val[N + M + 5], Fa[N + M + 5], Son[N + M + 5][2], rev[N + M + 5], Max[N + M + 5], Stack[N + M + 5], top;
inline void up(int u)
{
Max[u] = u;
if (Son[u][0] && Val[Max[Son[u][0]]] > Val[Max[u]]) Max[u] = Max[Son[u][0]];
if (Son[u][1] && Val[Max[Son[u][1]]] > Val[Max[u]]) Max[u] = Max[Son[u][1]];
}
inline void down(int u)
{
if (!rev[u]) return;
rev[Son[u][0]] ^= 1, rev[Son[u][1]] ^= 1, rev[u] ^= 1;
swap(Son[u][0], Son[u][1]);
}
inline int isroot(int u)
{
return (Son[Fa[u]][0] != u && Son[Fa[u]][1] != u);
}
inline void Rotate(int x)
{
int y = Fa[x], z = Fa[y];
int l = Son[y][1] == x, r = l ^ 1;
if (!isroot(y)) Son[z][Son[z][1] == y] = x;
Son[y][l] = Son[x][r], Fa[Son[x][r]] = y;
Son[x][r] = y, Fa[y] = x, Fa[x] = z;
up(y); up(x);
}
inline void Splay(int x)
{
Stack[top = 1] = x;
for (int y = x; !isroot(y); y = Fa[y]) Stack[++top] = Fa[y];
per(i, top, 1) down(Stack[i]);
while (!isroot(x))
{
int y = Fa[x], z = Fa[y];
if (!isroot(y))
{
if ((Son[z][1] == y) ^ (Son[y][1] == x)) Rotate(x);
Rotate(y);
}
Rotate(x);
}
}
inline void Access(int u)
{
for (int last = 0; u; last = u, u = Fa[u])
Splay(u), Son[u][1] = last, up(u);
}
inline void Make_Root(int u)
{
Access(u), Splay(u), rev[u] ^= 1;
}
inline int Find_Root(int u)
{
Access(u), Splay(u);
while (Son[u][0]) u = Son[u][0];
return u;
}
inline void Split(int x, int y)
{
Make_Root(x), Access(y), Splay(y);
}
inline void Link(int x, int y)
{
Make_Root(x);
if (Find_Root(y) == x) return;
Fa[x] = y;
}
inline void Cut(int x, int y)
{
Make_Root(x);
if (Find_Root(y) != x || Fa[x] != y || Son[x][1]) return;
Fa[x] = Son[y][0] = 0;
}
}LCT;
int sqz()
{
int n = read(), m = read(), cnt = 0, ans = INF;
rep(i, 1, m)
{
int u = read(), v = read(), a = read(), b = read();
if (u == v) continue;
Edge[++cnt] = node(u, v, a, b);
}
sort(Edge + 1, Edge + cnt + 1, cmp);
rep(i, 1, cnt)
{
LCT.Val[n + i] = Edge[i].b;
if (LCT.Find_Root(Edge[i].u) == LCT.Find_Root(Edge[i].v))
{
LCT.Split(Edge[i].u, Edge[i].v); int x = LCT.Max[Edge[i].v] - n;
if (LCT.Val[x + n] > Edge[i].b)
{
LCT.Cut(x + n, Edge[x].u), LCT.Cut(x + n, Edge[x].v);
LCT.Link(i + n, Edge[i].u), LCT.Link(i + n, Edge[i].v);
}
}
else LCT.Link(i + n, Edge[i].u), LCT.Link(i + n, Edge[i].v);
if (LCT.Find_Root(1) == LCT.Find_Root(n)) ans = min(ans, Edge[i].a + (LCT.Split(1, n), LCT.Val[LCT.Max[n]]));
}
printf("%d\n", ans == INF ? -1 : ans);
return 0;
}
|
