結果
| 問題 |
No.828 全方位神童数
|
| コンテスト | |
| ユーザー |
 kopricky
|
| 提出日時 | 2019-08-22 12:45:02 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 443 ms / 2,000 ms |
| コード長 | 24,207 bytes |
| コンパイル時間 | 2,099 ms |
| コンパイル使用メモリ | 186,296 KB |
| 実行使用メモリ | 110,400 KB |
| 最終ジャッジ日時 | 2024-10-12 06:37:30 |
| 合計ジャッジ時間 | 11,518 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 43 |
ソースコード
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
using namespace std;
template<typename S,typename T>auto&operator<<(ostream&o,pair<S,T>p){return o<<"{"<<p.fi<<","<<p.se<<"}";}
template<typename T>auto&operator<<(ostream&o,set<T>s){for(auto&e:s)o<<e<<" ";return o;}
template<typename S,typename T,typename U>
auto&operator<<(ostream&o,priority_queue<S,T,U>q){while(!q.empty())o<<q.top()<<" ",q.pop();return o;}
template<typename K,typename T>auto&operator<<(ostream&o,map<K,T>m){for(auto&e:m)o<<e<<" ";return o;}
template<typename T>auto&operator<<(ostream&o,vector<T>v){for(auto&e:v)o<<e<<" ";return o;}
void ashow(){cout<<endl;}template<typename T,typename...A>void ashow(T t,A...a){cout<<t<<" ";ashow(a...);}
typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<P> vp;
typedef vector<double> vd;
typedef vector<string> vs;
const int MAX_N = 200005;
template<class _Key, class _Tp, class _Hash, bool DOWNSIZE> class UnorderedMapIterator;
template<class _Key, class _Tp, class _Hash = hash<_Key>, bool DOWNSIZE = false>
class UnorderedMap
{
private:
using iterator = UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;
using value_type = _Tp;
using data_type = pair<_Key, _Tp>;
using aligned_pointer = typename aligned_storage<sizeof(value_type), alignof(value_type)>::type;
friend UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;
struct bucket {
_Key _key;
short int _dist;
bool _last, _end;
aligned_pointer _value_ptr;
bucket() noexcept : _dist(-1), _last(false), _end(false){}
// ~bucket(){ if(!empty()) _delete(); }
inline void clear() noexcept { _dist = -1; }
inline void _delete(){ _dist = -1, value_ptr()->~value_type(); }
inline bool empty() const noexcept { return (_dist == -1); }
inline value_type& value() noexcept {
return *reinterpret_cast<value_type*>(&_value_ptr);
}
inline value_type* value_ptr() noexcept {
return reinterpret_cast<value_type*>(&_value_ptr);
}
inline void new_value(const value_type& value){
new(&_value_ptr) value_type(value);
}
};
inline static unsigned int ceilpow2(unsigned int u) noexcept {
--u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8;
return (u | (u >> 16)) + 1;
}
inline static bucket *increment(bucket *cur) noexcept {
for(++cur; !cur->_end; ++cur){
if(!cur->empty()) break;
}
return cur;
}
inline bucket *next_bucket(bucket *cur) const noexcept {
return cur->_last ? _buckets : cur + 1;
}
inline unsigned int make_hash(const _Key& key) const noexcept {
return _Hash()(key);
}
inline float load_factor() const noexcept {
return (float)_data_count / _bucket_count;
}
bucket *insert_impl(bucket *cur, _Key key, short int dist, value_type value){
bucket *ret = cur;
bool flag = false;
while(true){
if(cur->empty()){
cur->_key = key, cur->_dist = dist, cur->new_value(value);
if(!flag) ret = cur, flag = true;
break;
}else if(dist > cur->_dist){
swap(key, cur->_key), swap(dist, cur->_dist), swap(value, cur->value());
if(!flag) ret = cur, flag = true;
}
++dist;
cur = next_bucket(cur);
}
return ret;
}
bucket *_find(const _Key& key, bool push=false){
bucket *cur = _buckets + (make_hash(key) & _mask);
short int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist;
cur = next_bucket(cur);
}
if(!push) return _buckets + _bucket_count;
++_data_count;
if(rehash_check()){
cur = _buckets + (make_hash(key) & _mask), dist = 0;
}
return insert_impl(cur, key, dist, _Tp());
}
bucket *_insert(const data_type& data){
const _Key& key = data.first;
bucket *cur = _buckets + (make_hash(key) & _mask);
short int dist = 0;
while(dist <= cur->_dist){
if(key == cur->_key) return cur;
++dist;
cur = next_bucket(cur);
}
++_data_count;
if(rehash_check()){
cur = _buckets + (make_hash(key) & _mask), dist = 0;
}
return insert_impl(cur, key, dist, data.second);
}
bucket *backward_shift(bucket *cur, bool next_ret){
bucket *next = next_bucket(cur), *ret = cur;
if(next->_dist < 1) return next_ret ? increment(cur) : cur;
do {
cur->_key = next->_key;
cur->_dist = next->_dist - 1;
cur->_value_ptr = next->_value_ptr;
cur = next, next = next_bucket(cur);
}while(next->_dist >= 1);
cur->clear();
return ret;
}
bucket *erase_impl(bucket *cur, bool next_ret){
assert(cur != _buckets + _bucket_count);
cur->_delete();
return backward_shift(cur, next_ret);
}
bucket *erase_itr(bucket *cur, bool next_ret = true){
--_data_count;
const _Key& key = cur->_key;
return erase_impl(rehash_check() ? _find(key) : cur, next_ret);
}
bucket *erase_key(const _Key& key, bool next_ret = true){
--_data_count;
rehash_check();
return erase_impl(_find(key), next_ret);
}
bool rehash_check(){
if(load_factor() >= MAX_LOAD_FACTOR){
rehash(_bucket_count * 2);
return true;
}else if(DOWNSIZE){
if(load_factor() <= MIN_LOAD_FACTOR && _bucket_count >= DOWNSIZE_THRESHOLD){
rehash(_bucket_count / 2);
return true;
}else{
return false;
}
}else{
return false;
}
}
void move_data(_Key key, aligned_pointer value_ptr){
bucket *cur = _buckets + (make_hash(key) & _mask);
short int dist = 0;
while(true){
if(cur->empty()){
cur->_key = key, cur->_dist = dist, cur->_value_ptr = value_ptr;
break;
}else if(dist > cur->_dist){
swap(key, cur->_key), swap(dist, cur->_dist), swap(value_ptr, cur->_value_ptr);
}
++dist;
cur = next_bucket(cur);
}
}
void rehash(unsigned int new_bucket_count){
UnorderedMap new_unordered_map(new_bucket_count);
new_unordered_map._data_count = _data_count;
for(bucket *cur = _buckets; !cur->_end; ++cur){
if(!cur->empty()){
new_unordered_map.move_data(cur->_key, cur->_value_ptr);
cur->clear();
}
}
swap(*this, new_unordered_map);
}
friend void swap(UnorderedMap& ump1, UnorderedMap& ump2){
swap(ump1._bucket_count, ump2._bucket_count);
swap(ump1._mask, ump2._mask);
swap(ump1._data_count, ump2._data_count);
swap(ump1._buckets, ump2._buckets);
}
private:
unsigned int _bucket_count, _mask, _data_count;
bucket *_buckets;
public:
const float MAX_LOAD_FACTOR = 0.5f;
const float MIN_LOAD_FACTOR = 0.1f;
const unsigned int DOWNSIZE_THRESHOLD = 16u;
UnorderedMap(unsigned int bucket_size = 1u)
: _bucket_count(ceilpow2(max(bucket_size, 1u))), _mask(_bucket_count - 1),
_data_count(0u), _buckets(new bucket[_bucket_count + 1]){
_buckets[_bucket_count - 1]._last = true, _buckets[_bucket_count]._end = true;
}
// ~UnorderedMap(){ delete[] _buckets; }
friend ostream& operator<< (ostream& os, UnorderedMap& ump) noexcept {
for(auto val : ump) os << '{' << val.first << ',' << val.second << "} ";
return os;
}
_Tp& operator[](const _Key& key){
return _find(key, true)->value();
}
const _Tp& at(const _Key& key){
bucket *res = _find(key);
if(res == _buckets + _bucket_count) __throw_out_of_range(__N("Unordered_Map::at"));
return res->value();
}
void clear(){
UnorderedMap new_unordered_map(1u);
swap(*this, new_unordered_map);
}
size_t size() const noexcept { return _data_count; }
size_t bucket_count() const noexcept { return _bucket_count; }
bool empty() const noexcept { return (_data_count == 0); }
iterator begin() const noexcept { return _buckets->empty() ? iterator(increment(_buckets)) : iterator(_buckets); }
iterator end() const noexcept { return iterator(_buckets + _bucket_count); }
iterator find(const _Key& key){ return iterator(_find(key)); }
iterator insert(const data_type& data){ return iterator(_insert(data)); }
iterator erase(const _Key& key){ return iterator(erase_key(key)); }
iterator erase(const iterator& itr){ return iterator(erase_itr(itr.bucket_ptr)); }
void simple_erase(const _Key& key){ erase_key(key, false); }
void simple_erase(const iterator& itr){ erase_itr(itr.bucket_ptr, false); }
// DEBUG 用
short int maximum_distance() const noexcept {
short int ret = -1;
for(bucket *cur = _buckets; !cur->_end; ++cur){
ret = max(ret, cur->_dist);
}
return ret;
}
};
template<class _Key, class _Tp, class _Hash, bool DOWNSIZE>
class UnorderedMapIterator {
private:
friend UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>;
typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *bucket_ptr;
using iterator_category = forward_iterator_tag;
using value_type = pair<const _Key, _Tp>;
using difference_type = ptrdiff_t;
using reference = pair<const _Key&, _Tp&>;
private:
UnorderedMapIterator(typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *_bucket_ptr)
noexcept : bucket_ptr(_bucket_ptr){}
public:
UnorderedMapIterator() noexcept : bucket_ptr(){}
UnorderedMapIterator(const UnorderedMapIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){}
UnorderedMapIterator& operator=(const UnorderedMapIterator& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
UnorderedMapIterator& operator=(const UnorderedMapIterator&& itr)
& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }
reference operator*() const noexcept { return {bucket_ptr->_key, bucket_ptr->value()}; }
UnorderedMapIterator& operator++() noexcept {
return bucket_ptr = UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(bucket_ptr), *this;
}
UnorderedMapIterator operator++(int) const noexcept {
return UnorderedMapIterator(UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(this->bucket_ptr));
}
bool operator==(const UnorderedMapIterator& itr) const noexcept { return !(*this != itr); };
bool operator!=(const UnorderedMapIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; }
};
template<typename _Tp> class BSTNode {
public:
int from, to, sz;
_Tp value, al, lazy;
BSTNode *left, *right, *par;
BSTNode(const int _from, const int _to) noexcept
: from(_from), to(_to), sz(0), value(id1), al(id2), lazy(id1),
left(nullptr), right(nullptr), par(nullptr){}
BSTNode(const int _from, const int _to, const _Tp& _value) noexcept
: from(_from), to(_to), sz(1), value(_value), al(value), lazy(id1),
left(nullptr), right(nullptr), par(nullptr){}
static const _Tp id1 = (_Tp)0;
static const _Tp id2 = (_Tp)0;
static void opr1(_Tp& arg1, const _Tp arg2) noexcept { arg1 += arg2; }
static _Tp opr2(const _Tp arg1, const _Tp arg2) noexcept { return arg1 + arg2; }
inline bool IsRoot() const noexcept { return !par; }
inline bool IsVertex() const noexcept { return from == to; }
void push() noexcept {
if(lazy != id1){
if(IsVertex()) opr1(value, lazy);
al += lazy * sz;
if(left) opr1(left->lazy, lazy);
if(right) opr1(right->lazy, lazy);
lazy = id1;
}
}
void eval() noexcept {
sz = IsVertex(), al = value;
if(left) left->push(), sz += left->sz, al = opr2(left->al, al);
if(right) right->push(), sz += right->sz, al = opr2(al, right->al);
}
void rotate(const bool right_) noexcept {
BSTNode *p = par, *g = p->par;
if(right_){
if((p->left = right)) right->par = p;
right = p, p->par = this;
}else{
if((p->right = left)) left->par = p;
left = p, p->par = this;
}
p->eval(), eval();
if(!(par = g)) return;
if(g->left == p) g->left = this;
if(g->right == p) g->right = this;
g->eval();
}
};
template<typename _Tp>
BSTNode<_Tp>* splay(BSTNode<_Tp> *u) noexcept {
if(!u) return nullptr;
while(!(u->IsRoot())){
BSTNode<_Tp> *p = u->par, *gp = p->par;
if(p->IsRoot()){ // zig
p->push(), u->push();
u->rotate((u == p->left));
}else{
gp->push(), p->push(), u->push();
bool flag = (u == p->left);
if((u == p->left) == (p == gp->left)){ // zig-zig
p->rotate(flag), u->rotate(flag);
}else{ // zig-zag
u->rotate(flag), u->rotate(!flag);
}
}
}
u->push();
return u;
}
template<typename _Tp>
BSTNode<_Tp>* join(BSTNode<_Tp> *root1, BSTNode<_Tp> *root2) noexcept {
if(!root1 || !root2) return root1 ? root1 : root2;
BSTNode<_Tp> *cur = nullptr, *nx = root1;
do{ cur = nx, cur->push(), nx = cur->right; }while(nx);
BSTNode<_Tp> *ver = splay(cur);
ver->right = root2, ver->eval(), root2->par = ver;
return ver;
}
template<typename _Tp>
pair<BSTNode<_Tp>*, BSTNode<_Tp>*> split_lower_bond(BSTNode<_Tp> *ver) noexcept {
BSTNode<_Tp> *res = splay(ver)->left;
ver->left = nullptr, ver->eval();
if(res) res->par = nullptr;
return make_pair(res, ver);
}
template<typename _Tp>
pair<BSTNode<_Tp>*, BSTNode<_Tp>*> split_upper_bond(BSTNode<_Tp> *ver) noexcept {
BSTNode<_Tp> *res = splay(ver)->right;
ver->right = nullptr, ver->eval();
if(res) res->par = nullptr;
return make_pair(ver, res);
}
template<typename T> class EulerTourTree {
private:
struct murmur_hash64 {
unsigned long long operator()(unsigned long long p) const {
const unsigned long long m = 0xc6a4a7935bd1e995; p *= m;
unsigned long long h = (p^(p>>47))*m;
return h = (h^(h>>47))*m, (h^(h>>47));
}
};
BSTNode<T>** vertex_set;
UnorderedMap<unsigned long long, pair<BSTNode<T>*, BSTNode<T>*>, murmur_hash64> edge_set;
inline static unsigned long long pair_to_ll(const int u, const int v){
return ((unsigned long long)(u) << 32) | v;
}
BSTNode<T> *reroot(BSTNode<T> *ver) noexcept {
BSTNode<T> *res = splay(ver)->left;
if(!res) return ver;
ver->left = nullptr, ver->eval();
while(ver->right) ver->push(), ver = ver->right;
splay(ver), ver->right = res, ver->eval(), res->par = ver;
return ver;
}
void link(BSTNode<T> *ver1, BSTNode<T> *ver2) noexcept {
BSTNode<T>* e1 = new BSTNode<T>(ver1->from, ver2->from);
BSTNode<T>* e2 = new BSTNode<T>(ver2->from, ver1->from);
edge_set[pair_to_ll(ver1->from, ver2->from)] = {e1, e2};
join(join(reroot(ver1), e1), join(reroot(ver2), e2));
}
void cut(BSTNode<T> *edge1, BSTNode<T> *edge2) noexcept {
splay(edge1), splay(edge2);
BSTNode<T> *p = edge1->par;
bool _right = (edge1 == edge2->right);
if(p != edge2){
_right = (p == edge2->right);
p->par = nullptr, edge1->rotate((edge1 == p->left));
}
if(edge1->left) edge1->left->par = nullptr;
if(edge1->right) edge1->right->par = nullptr;
if(_right){
if(edge2->left) edge2->left->par = nullptr;
join(edge2->left, edge1->right);
}else{
if(edge2->right) edge2->right->par = nullptr;
join(edge1->left, edge2->right);
}
// delete edge1; delete edge2;
}
bool IsConnected(BSTNode<T> *ver1, BSTNode<T> *ver2) noexcept {
splay(ver1), splay(ver2);
return ver1->par;
}
T& get(BSTNode<T> *ver) noexcept { return splay(ver)->value; }
void range(BSTNode<T> *edge1, BSTNode<T> *edge2, const T& val) noexcept {
auto res1 = split_lower_bond(edge1);
auto res2 = split_upper_bond(edge2);
BSTNode<T>::opr1(res2.first->lazy, val);
join(join(res1.first,res2.first), res2.second);
}
T query(BSTNode<T> *edge1, BSTNode<T> *edge2) noexcept {
auto res1 = split_lower_bond(edge1);
auto res2 = split_upper_bond(edge2);
T res = res2.first->al;
return join(join(res1.first,res2.first), res2.second), res;
}
public:
const int V;
EulerTourTree(const vector<T>& ver_value, bool helper=false) noexcept : V((int)ver_value.size()){
vertex_set = new BSTNode<T>*[V];
for(int i = 0; i < V; i++) vertex_set[i] = new BSTNode<T>(i, i, ver_value[i]);
if(helper) G.resize(V);
}
// ~EulerTourTree(){
// for(auto it : edge_set){
// delete (it.second).first;
// delete (it.second).second;
// }
// for(int i = 0; i < V; ++i) delete vertex_set[i];
// delete[] vertex_set;
// }
// 根を node_id にする
void reroot(const int node_id) noexcept { reroot(vertex_set[node_id]); }
// 辺(node1_id, node2_id) を追加
void link(int node1_id, int node2_id) noexcept {
if(node1_id > node2_id) swap(node1_id, node2_id);
link(vertex_set[node1_id], vertex_set[node2_id]);
}
// 辺(node1_id, node2_id) を削除(逆向きでも問題ない)
void cut(int node1_id, int node2_id){
if(node1_id > node2_id) swap(node1_id, node2_id);
auto it = edge_set.find(pair_to_ll(node1_id, node2_id));
assert(it != edge_set.end());
BSTNode<T> *edge1 = ((*it).second).first, *edge2 = ((*it).second).second;
edge_set.simple_erase(it);
cut(edge1, edge2);
}
// node1_id と node2_id が同じ木(連結成分)に属するか
bool IsConnected(const int node1_id, const int node2_id) noexcept {
if(node1_id == node2_id) return true;
return IsConnected(vertex_set[node1_id], vertex_set[node2_id]);
}
// 頂点 ver_id の値を取得
T& get(int ver_id) noexcept { return get(vertex_set[ver_id]); }
// 頂点 ver_id の存在する連結成分内の頂点全体に val を加える
void component_range(const int ver_id, const T& val){ range(ver_id, -1, val); }
// 親が par_id であるような頂点 ver_id の部分木内に存在する頂点全体に val を加える
void range(const int ver_id, const int par_id, const T& val){
if(par_id < 0) return BSTNode<T>::opr1(splay(vertex_set[ver_id])->lazy, val);
if(ver_id < par_id){
auto it = edge_set.find(pair_to_ll(ver_id, par_id));
assert(it != edge_set.end());
range(((*it).second).second, ((*it).second).first, val);
}else{
auto it = edge_set.find(pair_to_ll(ver_id, par_id));
assert(it != edge_set.end());
range(((*it).second).second, ((*it).second).first, val);
}
}
// 頂点 ver_id の存在する連結成分内の頂点全体の総和を取得
T component_query(const int ver_id){ return query(ver_id, -1); }
// 親が par_id であるような頂点 ver_id の部分木内に存在する頂点全体の総和を取得
T query(const int ver_id, const int par_id){
if(par_id < 0) return splay(vertex_set[ver_id])->al;
if(ver_id < par_id){
auto it = edge_set.find(pair_to_ll(ver_id, par_id));
assert(it != edge_set.end());
return query(((*it).second).second, ((*it).second).first);
}else{
auto it = edge_set.find({par_id, ver_id});
assert(it != edge_set.end());
return query(((*it).second).second, ((*it).second).first);
}
}
// ヘルパー関数
vector<vector<int> > G;
void add_edge(const int u, const int v) noexcept { G[u].push_back(v), G[v].push_back(u); }
void dfs(const int u, const int p, const BSTNode<T> *cur,
vector<int>& parent, vector<BSTNode<T>*>& nodes) noexcept {
parent[u] = p;
nodes.push_back(vertex_set[u]);
for(auto& v : G[u]){
if(v != p){
BSTNode<T>* e1 = new BSTNode<T>(u, v);
nodes.push_back(e1);
dfs(v, u, cur, parent, nodes);
BSTNode<T>* e2 = new BSTNode<T>(v, u);
if(u < v) edge_set[pair_to_ll(u, v)] = {e1, e2};
else edge_set[pair_to_ll(v, u)] = {e2, e1};
nodes.push_back(e2);
}
}
}
void bst_build(vector<BSTNode<T>* >& nodes) noexcept {
int i, n = (int)nodes.size(), st = 2, isolate = ((n % 4 == 1) ? (n-1) : -1);
while(st <= n){
for(i = st-1; i < n; i += 2*st){
nodes[i]->left = nodes[i-st/2], nodes[i-st/2]->par = nodes[i];
if(i+st/2 < n) nodes[i]->right = nodes[i+st/2], nodes[i+st/2]->par = nodes[i];
else if(isolate >= 0) nodes[i]->right = nodes[isolate], nodes[isolate]->par = nodes[i];
nodes[i]->eval();
}
isolate = ((n % (4*st) >= st && (n % (4*st) < 2*st)) ? (i-2*st): isolate);
st <<= 1;
}
}
// _root を根とする木を構築(親の vector を返す)
vector<int> build_tree(const int _root) noexcept {
vector<int> parent(V, -1);
vector<BSTNode<T>* > nodes;
BSTNode<T> *cur = nullptr;
dfs(_root, -1, cur, parent, nodes);
bst_build(nodes);
return parent;
}
// 森を構築
vector<int> build_forest() noexcept {
vector<int> parent(V, -1);
for(int i = 0; i < V; i++){
if(parent[i] < 0){
vector<BSTNode<T>* > nodes;
BSTNode<T> *cur = nullptr;
dfs(i, -1, cur, parent, nodes);
bst_build(nodes);
}
}
return parent;
}
private:
void check_dfs(const BSTNode<T>* cur) const noexcept {
cur->push();
if(cur->left) check_dfs(cur->left);
if(cur->IsVertex()) cout <<"{" << (cur->from) << "," << (cur->value) << "} ";
if(cur->right) check_dfs(cur->right);
}
};
#define getchar getchar_unlocked
#define putchar putchar_unlocked
inline int in() {
int n = 0; short c;
while ((c = getchar()) >= '0') n = n * 10 + c - '0';
return n;
}
inline void out(int n) {
short res[10], i = 0;
do { res[i++] = n % 10, n /= 10; } while (n);
while (i) putchar(res[--i] + '0');
putchar('\n');
}
int r[MAX_N];
int main()
{
int n = in();
rep(i,n) r[i] = in();
EulerTourTree<int> et(vi(n, 0), true);
rep(i,n-1){
int u = in(), v = in();
et.add_edge(u-1, v-1);
}
auto par = et.build_tree(0);
rrep(i,n){
et.component_range(i, 1);
for(auto& to : et.G[i]){
if(to < i) et.cut(to, i);
}
}
int ans = 1;
rep(i,n){
ans = (ll)ans * (et.get(i) + r[i]) % MOD;
}
out(ans);
return 0;
}