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struct GM {
vector<vector<int>> adj;
// pairs ist der gematchte knoten oder n
vector<int> pairs, first, que;
vector<pair<int, int>> label;
int head, tail;
GM(int n) : adj(n), pairs(n + 1, n), first(n + 1, n),
que(n), label(n + 1, {-1, -1}) {}
void rematch(int u, int v) {
int t = pairs[u]; pairs[u] = v;
if (pairs[t] != u) return;
if (label[u].second == -1) {
pairs[t] = label[u].first;
rematch(pairs[t], t);
} else {
auto [x, y] = label[u];
rematch(x, y);
rematch(y, x);
}}
int findFirst(int v) {
return label[first[v]].first < 0 ? first[v]
: first[v] = findFirst(first[v]);
}
void relabel(int x, int y) {
int r = findFirst(x);
int s = findFirst(y);
if (r == s) return;
auto h = label[r] = label[s] = {~x, y};
int join;
while (true) {
if (s != sz(adj)) swap(r, s);
r = findFirst(label[pairs[r]].first);
if (label[r] == h) {
join = r;
break;
} else {
label[r] = h;
}}
for (int v : {first[x], first[y]}) {
for (; v != join; v = first[label[pairs[v]].first]) {
label[v] = {x, y};
first[v] = join;
que[tail++] = v;
}}}
bool augment(int v) {
label[v] = {sz(adj), -1};
first[v] = sz(adj);
head = tail = 0;
for (que[tail++] = v; head < tail;) {
int x = que[head++];
for (int y : adj[x]) {
if (pairs[y] == sz(adj) && y != v) {
pairs[y] = x;
rematch(x, y);
return true;
} else if (label[y].first >= 0) {
relabel(x, y);
} else if (label[pairs[y]].first == -1) {
label[pairs[y]].first = x;
first[pairs[y]] = y;
que[tail++] = pairs[y];
}}}
return false;
}
int match() {
int matching = head = tail = 0;
for (int v = 0; v < sz(adj); v++) {
if (pairs[v] < sz(adj) || !augment(v)) continue;
matching++;
for (int i = 0; i < tail; i++)
label[que[i]] = label[pairs[que[i]]] = {-1, -1};
label[sz(adj)] = {-1, -1};
}
return matching;
}
};
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