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| #include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#define debug(...) fprintf(stdout, ##__VA_ARGS__)
#define debag(...) fprintf(stderr, ##__VA_ARGS__)
#else
#define debug(...) void(0)
#define debag(...) void(0)
#endif
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
#define fi first
#define se second
#define N 200010
struct node {
int u, v, a, b;
}e[N];
int n, m, i, j, k, T;
int ans, a[N], u, v;
namespace LCT {
#define ls(x) (son[x][0])
#define rs(x) (son[x][1])
int son[N][2], rev[N], mx[N], fa[N];
void push_down(int x) {
if(rev[x]) {
swap(ls(x), rs(x));
if(ls(x)) rev[ls(x)] ^= 1;
if(rs(x)) rev[rs(x)] ^= 1;
rev[x] = 0;
}
}
void push_up(int x) {
mx[x] = x;
if(a[mx[ls(x)]] > a[mx[x]]) mx[x] = mx[ls(x)];
if(a[mx[rs(x)]] > a[mx[x]]) mx[x] = mx[rs(x)];
}
bool isRoot(int x) {
if(!fa[x]) return true;
return ls(fa[x]) != x && rs(fa[x]) != x;
}
int zh(int x) {
return rs(fa[x]) == x;
}
void Rotate(int x) {
int y = fa[x], z = fa[y];
int k = zh(x), w = son[x][k ^ 1];
if(z && !isRoot(y)) son[z][zh(y)] = x;
if(w) fa[w] = y, son[y][k] = w; else son[y][k] = 0;
fa[x] = z; fa[y] = x; son[x][k ^ 1] = y;
push_up(y); push_up(x); push_up(z);
}
void Splay(int x) {
stack<int>sta; sta.push(x);
for(int y = x; !isRoot(y); y = fa[y]) sta.push(fa[y]);
while(!sta.empty()) push_down(sta.top()), sta.pop();
while(!isRoot(x)) {
int y = fa[x];
if(!isRoot(y)) {
if(zh(y) == zh(x)) Rotate(y);
else Rotate(x);
}
Rotate(x);
}
}
void access(int x) {
debug("access(%d)\n", x);
for(int y = 0; x; y = x, x = fa[x]) {
Splay(x); rs(x) = y; push_up(x);
}
}
void makeRoot(int x) {
access(x); Splay(x); rev[x] ^= 1;
}
int findRoot(int x) {
access(x); Splay(x);
while(push_down(x), ls(x)) x = ls(x);
Splay(x);
return x;
}
bool check(int x, int y) {
makeRoot(x);
return findRoot(y) == x;
}
void Link(int x, int y) {
debug("Link(%d %d)\n", x, y);
makeRoot(x); fa[x] = y;
}
void Delete(int x) {
makeRoot(x); Splay(x); push_down(x);
fa[ls(x)] = fa[rs(x)] = 0; ls(x) = rs(x) = 0;
}
int Qrymax(int x, int y) {
makeRoot(x); access(y); Splay(y);
int z = mx[y]; Splay(z);
return z;
}
void print() {
int i;
#ifdef LOCAL
debug("(%d %d %d | %d %d)\n", fa[1], ls(1), rs(1), a[1], mx[1]);
for(i = 1; i <= n + m; ++i)
if(fa[i] || ls(i) || rs(i)) debug("fa[%d] = %d(%d)(%d %d) || %d %d\n",
i, fa[i], isRoot(i), ls(i), rs(i), a[i], mx[i]);
debug("----------------------------------------\n");
#endif
}
}
signed main()
{
#ifdef LOCAL
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#endif
n = read(); m = read(); ans = 1e9;
for(i = 1; i <= n + m; ++i) LCT :: mx[i] = i;
for(i = 1; i <= m; ++i) {
e[i].u = read(); e[i].v = read();
e[i].a = read(); e[i].b = read();
}
sort(e + 1, e + m + 1, [] (node x, node y) { return x.a < y.a; });
for(i = 1; i <= m; ++i) {
u = e[i].u; v = e[i].v; a[i + n] = e[i].b;
debug("(%d %d) %d %d\n", u, v, e[i].a, e[i].b);
if(!LCT :: check(u, v)) {
LCT :: Link(u, i + n);
LCT :: Link(v, i + n);
}
else {
int x = LCT :: Qrymax(u, v);
if(a[x] > e[i].b) {
LCT :: Delete(x);
LCT :: Link(u, i + n), LCT :: Link(v, i + n);
}
}
if(LCT :: check(1, n)) {
int x = LCT :: Qrymax(1, n);
debug("#### %d + %d(%d)\n", e[i].a, a[x]);
ans = min(ans, e[i].a + a[x]);
}
}
printf("%d", ans == 1e9 ? -1 : ans);
return 0;
}
|
