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struct item {
int key, prior;
item *l, *r;
item() { }
item (int key, int prior) : key(key), prior(prior), l(NULL), r(NULL) { }
};
void split (item *t, int key, item *l, item *r) {
if (!t) l = r = NULL;
else if (key < t->key) split(t->l, key, l, t->l), r = t;
else split(t->r, key, t->r, r), l = t;
}
void insert (item *t, item *it) {
if (!t) t = it;
else if (it->prior > t->prior) split(t, it->key, it->l, it->r), t = it;
else insert(it->key < t->key ? t->l : t->r, it);
}
void merge (item *t, item *l, item *r) {
if (!l || !r) t = l ? l : r;
else if (l->prior > r->prior) merge(l->r, l->r, r), t = l;
else merge(r->l, l, r->l), t = r;
}
void erase (item *t, int key) {
if (t->key == key) merge (t, t->l, t->r);
else erase(key < t->key ? t->l : t->r, key);
}
item *unite (item *l, item *r) {
if (!l || !r) return l ? l : r;
if (l->prior < r->prior) swap(l, r);
item * lt, rt;
split(r, l->key, lt, rt);
l->l = unite(l->l, lt);
l->r = unite(l->r, rt);
return l;
}
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