結果
| 問題 | No.1078 I love Matrix Construction |
| ユーザー |
 kjnh10
|
| 提出日時 | 2020-06-16 19:46:20 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 605 ms / 2,000 ms |
| コード長 | 23,983 bytes |
| コンパイル時間 | 3,417 ms |
| コンパイル使用メモリ | 249,468 KB |
| 実行使用メモリ | 254,604 KB |
| 最終ジャッジ日時 | 2024-07-03 11:57:34 |
| 合計ジャッジ時間 | 10,315 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,944 KB |
| testcase_02 | AC | 72 ms
40,336 KB |
| testcase_03 | AC | 203 ms
101,456 KB |
| testcase_04 | AC | 288 ms
138,336 KB |
| testcase_05 | AC | 243 ms
115,244 KB |
| testcase_06 | AC | 67 ms
39,192 KB |
| testcase_07 | AC | 24 ms
16,936 KB |
| testcase_08 | AC | 242 ms
114,804 KB |
| testcase_09 | AC | 11 ms
8,688 KB |
| testcase_10 | AC | 605 ms
254,604 KB |
| testcase_11 | AC | 309 ms
145,224 KB |
| testcase_12 | AC | 490 ms
213,504 KB |
| testcase_13 | AC | 539 ms
239,248 KB |
| testcase_14 | AC | 345 ms
170,504 KB |
| testcase_15 | AC | 498 ms
226,924 KB |
| testcase_16 | AC | 20 ms
13,948 KB |
| testcase_17 | AC | 2 ms
6,940 KB |
| testcase_18 | AC | 48 ms
30,180 KB |
| testcase_19 | AC | 116 ms
64,732 KB |
| testcase_20 | AC | 123 ms
63,796 KB |
| testcase_21 | AC | 5 ms
6,940 KB |
ソースコード
#line 2 "header.hpp"
//%snippet.set('header')%
//%snippet.fold()%
#ifndef HEADER_H
#define HEADER_H
// template version 2.0
using namespace std;
#include <bits/stdc++.h>
// varibable settings
const long long INF = 1e18;
template <class T> constexpr T inf = numeric_limits<T>::max() / 2.1;
#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _rrep(i, n) rrepi(i, 0, n)
#define rrepi(i, a, b) for (ll i = (ll)((b)-1); i >= (ll)(a); --i)
#define r_rep(...) _overload3(__VA_ARGS__, rrepi, _rrep, )(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
#define ub upper_bound
#define lb lower_bound
#define lpos(A, x) (lower_bound(all(A), x) - A.begin())
#define upos(A, x) (upper_bound(all(A), x) - A.begin())
template <class T> inline void chmax(T &a, const T &b) { if ((a) < (b)) (a) = (b); }
template <class T> inline void chmin(T &a, const T &b) { if ((a) > (b)) (a) = (b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector<decltype(cont)>(x, cont); }
#define cdiv(a, b) (((a) + (b)-1) / (b))
#define is_in(x, a, b) ((a) <= (x) && (x) < (b))
#define uni(x) sort(all(x)); x.erase(unique(all(x)), x.end())
#define slice(l, r) substr(l, r - l)
typedef long long ll;
typedef long double ld;
using vl = vector<ll>;
using vvl = vector<vl>;
using pll = pair<ll, ll>;
template <typename T>
using PQ = priority_queue<T, vector<T>, greater<T>>;
void check_input() { assert(cin.eof() == 0); int tmp; cin >> tmp; assert(cin.eof() == 1); }
#if defined(PCM) || defined(LOCAL)
#else
#define dump(...) ;
#define dump_1d(...) ;
#define dump_2d(...) ;
#define cerrendl ;
#endif
#endif /* HEADER_H */
//%snippet.end()%
#line 2 "solve.cpp"
template<class T=ll> using vec = vector<T>;
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;
// snippet:segment_tree {{{
template <typename T> struct SegmentTree { // {{{
private:
using F = function<T(T, T)>;
int n; // 元の配列のサイズ
int N; // n以上の最小の2冪
vector<T> node;
F merge;
T identity;
public:
SegmentTree() {}
SegmentTree(vector<T> a, F f, T id) : merge(f), identity(id) {
n = a.size();
N = 1;
while (N < n) N *= 2;
node.resize(2 * N - 1, identity);
for (int i = 0; i < n; i++) node[i + N - 1] = a[i];
for (int i = N - 2; i >= 0; i--)
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
SegmentTree(int n, F f, T id) : SegmentTree(vector<T>(n, id), f, id) {}
T& operator[](int i) { return node[i + N - 1]; }
void update(int i, T val) {
i += (N - 1);
node[i] = val;
while (i > 0) {
i = (i - 1) / 2;
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
}
void add(int i, T val) {
i += (N - 1);
node[i] += val;
while (i > 0) {
i = (i - 1) / 2;
node[i] = merge(node[2 * i + 1], node[2 * i + 2]);
}
}
// query for [a, b)
T query(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (r <= a || b <= l) return identity;
if (a <= l && r <= b) return node[k];
T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
return merge(vl, vr);
}
// find most right element for [a, b)
int find_mr(int a, int b, function<bool(T)> is_ok, int k = 0, int l = 0, int r = -1){
if (r < 0) r = N;
if (r <= a || b <= l || !is_ok(node[k])) return a-1;
if (k >= N-1) return k - (N-1); // leaf
T vr = find_mr(a, b, is_ok, 2 * k + 2, (l + r) / 2, r);
if (vr != a-1) return vr;
T vl = find_mr(a, b, is_ok, 2 * k + 1, l, (l + r) / 2);
return vl;
}
// find most left element for [a, b)
int find_ml(int a, int b, function<bool(T)> is_ok, int k = 0, int l = 0, int r = -1){
// find most left
if (r < 0) r = N;
if (r <= a || b <= l || !is_ok(node[k])) return b;
if (k >= N-1) return k - (N-1); // leaf
T vl = find_ml(a, b, is_ok, 2 * k + 1, l, (l + r) / 2);
if (vl != b) return vl;
T vr = find_ml(a, b, is_ok, 2 * k + 2, (l + r) / 2, r);
return vr;
}
#if defined(PCM) || defined(LOCAL)
friend ostream& operator<<(ostream& os, SegmentTree<T>& sg) { //
os << "[";
for (int i = 0; i < sg.n; i++) {
os << sg[i] << (i == sg.n - 1 ? "]\n" : ", ");
}
return os;
}
#endif
};/*}}}*/
// sample of initialize SegmentTree:
// -----------------------------------------------
// auto mymin=[](auto a, auto b){return min(a,b);};
// SegmentTree<ll> seg(a, mymin, 1e18);
// auto mymax=[](auto a, auto b){return max(a,b);};
// SegmentTree<ll> seg(a, mymax, -1e18);
// auto add=[](auto a, auto b){return a+b;};
// SegmentTree<ll> seg(a, add, 0);
// -----------------------------------------------
// snippet:segment_tree }}}
// snippet:edge {{{
template<class Cost=ll>
struct Edge {
int from, to;
Cost cost;
int idx;
Edge(){};
Edge(int from, int to, Cost cost, int idx)
: from(from), to(to), cost(cost), idx(idx) {}
friend ostream& operator<<(ostream& os, const Edge& e) {
// os << "(f:" << e.from << ", t:" << e.to << ", c:" << e.cost << ", i" << e.idx << ")"; // detailed
os << "(" << e.from << "," << e.to << ")";
return os;
}
};
// snippet:edge }}}
// snippet:UnionFind {{{
struct UnionFind {
vector<int> par; // par[x]: parent of x. if root, -size.
int gcount; // count of groups
UnionFind() {}
UnionFind(int _n) : par(_n, -1), gcount(_n) {}
bool merge(int x, int y) {
x = root(x);
y = root(y);
if (x != y) {
if (par[y] < par[x]) swap(x, y);
par[x] += par[y];
par[y] = x;
gcount--;
}
return x != y;
}
int root(int x) {
if (is_root(x)){
return x;
}
else{
return par[x] = root(par[x]); // 経路圧縮
// return root(par[x]); // 経路圧縮なし
}
}
bool is_root(int x) { return par[x] < 0; }
bool same(int x, int y) { return root(x) == root(y); }
int size(int x) { return -par[root(x)]; }
#if defined(PCM) || defined(LOCAL) // {{{
friend ostream& operator<<(ostream& os, UnionFind& uf) {
map<int, vector<int>> group;
rep(i, sz(uf.par)) { group[uf.root(i)].pb(i); }
os << endl;
each(g, group) { os << g << endl; }
return os;
}
#endif // }}}
};
// snippet:UnionFind }}}
// snippet:tree {{{
template<class Cost=ll>
struct tree {
int n;
int root;
vector<int> par; // par[i]: dfs木における親
vector<Cost> cost; // par[i]: dfs木における親への辺のコスト
vector<int> dfstrv; // dfstrv[i]: dfs木でi番目に訪れるノード。dpはこれを逆順に回す
vector<int> ord; // ord[u]: uのdfs木における訪問順
vector<int> end; // end[u]: uのdfs終了時のカウンター
vector<int> psize; // psize[u]: uのpartial tree size
// uの部分木は[ord[u], end[u])
// ordとdfstrvは逆変換
vector<int> depth; // depth[i]: dfs木でのiの深さ
vector<Cost> ldepth; // ldepth[i]: dfs木でのrootからの距離
vector<vector<Edge<Cost>>> adj_list; // 辺(隣接リスト)
auto operator[](int pos) const { return adj_list[pos]; }
vector<vector<int>> children;
vector<int> euler_tour;
vector<int> et_fpos; // euler_tour first occurence position
SegmentTree<int> _seg; // seg(map(ord, euler_tour), mymin, 1e18)
vector<int> head_of_comp;
int _counter = 0;
tree(){};/*{{{*/
tree(int n)
: n(n),
par(n),
cost(n),
ord(n),
end(n),
psize(n),
depth(n),
ldepth(n),
adj_list(n),
children(n),
et_fpos(n),
head_of_comp(n){};/*}}}*/
void add_edge(int u, int v, Cost cost, int idx=-1) { /*{{{*/
adj_list[u].emplace_back(u, v, cost, idx);
adj_list[v].emplace_back(v, u, cost, idx);
} /*}}}*/
void add_edge(int u, int v) { /*{{{*/
adj_list[u].emplace_back(u, v, 1, -1);
adj_list[v].emplace_back(v, u, 1, -1);
} /*}}}*/
void build(int _root) { /*{{{*/
root = _root;
_counter = 0;
par[root] = -1;
// cost[root] = -1;
_dfs_psize(root, -1);
_dfs_tree(root, -1, root);
_dfs_et(root);
vector<int> ini(2 * n - 1);
rep(i, 2 * n - 1) ini[i] = ord[euler_tour[i]];
_seg = SegmentTree<int>(
ini, [](auto a, auto b) { return min(a, b); }, numeric_limits<int>().max());
} /*}}}*/
int _dfs_psize(int u, int pre) { /*{{{*/
psize[u] = 1;
each(edge, adj_list[u]) {
if (edge.to == pre) continue;
psize[u] += _dfs_psize(edge.to, u);
}
return psize[u];
} /*}}}*/
void _dfs_tree(int u, int pre, int head_node) { /*{{{*/
dfstrv.pb(u);
ord[u] = _counter;
if (pre != -1) {
depth[u] = depth[pre] + 1;
ldepth[u] = ldepth[pre] + cost[u];
}
_counter++;
{
// set most heavy child to top
int max_psize = 0;
int most_heavy_i = -1;
rep(i, sz(adj_list[u])) {
if (adj_list[u][i].to == pre) continue;
if (psize[adj_list[u][i].to] > max_psize) {
most_heavy_i = i;
max_psize = psize[adj_list[u][i].to];
}
}
if (most_heavy_i != -1) swap(adj_list[u][most_heavy_i], adj_list[u][0]);
}
head_of_comp[u] = head_node;
rep(i, sz(adj_list[u])) {
int v = adj_list[u][i].to;
if (v == pre) continue;
children[u].pb(v);
par[v] = u;
cost[v] = adj_list[u][i].cost;
if (i == 0)
_dfs_tree(v, u, head_node); // continue components
else
_dfs_tree(v, u, v); // new
}
end[u] = _counter;
} /*}}}*/
void _dfs_et(int u) { /*{{{*/
et_fpos[u] = euler_tour.size();
euler_tour.pb(u);
each(v, children[u]) {
_dfs_et(v);
euler_tour.pb(u);
}
} /*}}}*/
int lca(int u, int v) { /*{{{*/
if (u == v) return u;
if (et_fpos[u] > et_fpos[v]) swap(u, v);
return dfstrv[_seg.query(et_fpos[u], et_fpos[v])];
} /*}}}*/
int dist(int u, int v) { /*{{{*/
int p = lca(u, v);
return depth[u] + depth[v] - 2 * depth[p];
} /*}}}*/
Cost ldist(int u, int v) { // length dist{{{
int p = lca(u, v);
return ldepth[u] + ldepth[v] - 2 * ldepth[p];
} /*}}}*/
pair<int, int> diameter() { /*{{{*/
int u, v;
Cost max_len = *max_element(all(ldepth));
rep(i, n) {
if (ldepth[i] == max_len) {
u = i;
break;
}
}
Cost md = -1;
rep(i, n) {
Cost d = ldist(u, i);
if (d > md) {
v = i;
md = d;
}
}
return mp(u, v);
} /*}}}*/
vector<pair<int, int>> hld_path(int u, int v, bool for_edge=true) { //{{{
// 閉区間をvectorで返す。for_edge=trueでlcaは除いて返すことに注意。
vector<pair<int, int>> res;
while (head_of_comp[u] != head_of_comp[v]) {
if (depth[head_of_comp[u]] < depth[head_of_comp[v]]) {
res.push_back({ord[head_of_comp[v]], ord[v]});
v = par[head_of_comp[v]];
} else {
res.push_back({ord[head_of_comp[u]], ord[u]});
u = par[head_of_comp[u]];
}
}
res.push_back({min(ord[u], ord[v]) + (for_edge?1:0), max(ord[u], ord[v])});
return res;
} //}}}
#if defined(PCM) || defined(LOCAL) /*{{{*/
friend ostream& operator<<(ostream& os, const tree& tr) {
os << endl;
os << "par: " << tr.par << endl;
os << "cost: " << tr.cost << endl;
os << "dfstrv: " << tr.dfstrv << endl;
os << "ord: " << tr.ord << endl;
os << "end: " << tr.end << endl;
os << "depth: " << tr.depth << endl;
os << "children: " << tr.children << endl;
os << "euler_tour: " << tr.euler_tour << endl;
os << "et_fpos: " << tr.et_fpos << endl;
os << "head_of_comp:" << tr.head_of_comp << endl;
return os;
}
#endif /*}}}*/
};
// snippet:tree }}}
// snippet:Graph {{{
template<class Cost=ll>
struct Graph {
using Pos = int; // int以外には対応しない。
int n; // 頂点数
vector<vector<Edge<Cost>>> adj_list;
auto operator[](Pos pos) const { return adj_list[pos]; }
vector<Edge<Cost>> edges;
tree<Cost> tr;
Pos root;
vector<int> _used_in_dfs;
vector<int> lowlink;
Cost zerocost;
Cost infcost;
Graph() {}
Graph(int _n) : n(_n), adj_list(_n), tr(n), _used_in_dfs(n), zerocost(0LL), infcost(INF) { }
Graph(int _n, Cost zc, Cost ic) : n(_n), adj_list(_n), tr(n), _used_in_dfs(n), zerocost(zc), infcost(ic) { }
void add_edge(Pos from, Pos to, Cost cost, int idx=-1) {/*{{{*/
adj_list[from].emplace_back(from, to, cost, idx);
edges.emplace_back(from, to, cost, idx);
}
void add_edge(Pos from, Pos to) { // for ll
dump(from, to);
adj_list[from].emplace_back(from, to, 1, -1);
edges.emplace_back(from, to, 1, -1);
}/*}}}*/
void build_tree(Pos _root) {/*{{{*/
root = _root;
_dfs_tree(root);
tr.build(root);
_make_lowlink();
}/*}}}*/
vector<int> make_bipartite() {/*{{{*/
UnionFind buf(2 * n);
rep(u, n) {
each(e, adj_list[u]) {
buf.merge(u, e.to + n);
buf.merge(e.to, u + n);
}
}
vector<int> res(n, -1);
rep(u, n) {
if (buf.same(u, u + n)) return res;
}
rep(u, n) {
if (buf.same(0, u)) res[u] = 0;
else res[u] = 1;
}
return res;
}/*}}}*/
void _dfs_tree(Pos u) {/*{{{*/
_used_in_dfs[u] = 1;
each(e, adj_list[u]) {
if (_used_in_dfs[e.to]) continue;
tr.add_edge(u, e.to, e.cost);
_dfs_tree(e.to);
}
}/*}}}*/
void _make_lowlink() {/*{{{*/
lowlink = vector<Pos>(n, numeric_limits<Pos>().max());
r_rep(i, n) {
Pos u = tr.dfstrv[i];
chmin(lowlink[u], tr.ord[u]);
each(e, adj_list[u]) {
if (e.to == tr.par[u])
continue;
else if (tr.ord[e.to] < tr.ord[u]) {
chmin(lowlink[u], tr.ord[e.to]);
} else {
chmin(lowlink[u], lowlink[e.to]);
}
}
}
}/*}}}*/
vector<Pos> get_articulation_points() {/*{{{*/
if (sz(lowlink) == 0) throw("make_lowlik() beforehand");
vector<Pos> res;
if (sz(tr.children[root]) > 1) {
res.push_back(root);
}
rep(u, 0, n) {
if (u == root) continue;
bool is_kan = false;
each(v, tr.children[u]) {
if (tr.ord[u] <= lowlink[v]) {
is_kan = true;
}
}
if (is_kan) res.push_back(u);
}
return res;
}/*}}}*/
vector<Edge<Cost>> get_bridges() {/*{{{*/
if (sz(lowlink) == 0) throw("make_lowlik() beforehand");
vector<Edge<Cost>> res;
each(edge, edges){
if (tr.ord[edge.from] < lowlink[edge.to]) res.push_back(edge);
}
return res;
}/*}}}*/
vector<Edge<Cost>> kruskal_tree() {/*{{{*/
// 使用される辺のvectorを返す
vector<Edge<Cost>> res(n - 1);
sort(all(edges), [&](auto l, auto r) { return l.cost < r.cost; });
UnionFind uf(n);
Cost total_cost = zerocost;
int idx = 0;
each(e, edges) {
if (uf.same(e.from, e.to)) continue;
uf.merge(e.from, e.to);
total_cost = total_cost + e.cost;
res[idx] = e;
idx++;
}
assert(idx == n - 1);
return res;
}/*}}}*/
vector<Cost> dijkstra(vector<Pos> starts) { // 多点スタート{{{
vector<Cost> dist(n, infcost); // 最短距離
PQ<pair<Cost, Pos>> pq;
each(start, starts) {
dist[start] = zerocost;
pq.push(make_pair(zerocost, start));
}
while (!pq.empty()) {
auto cp = pq.top();
pq.pop();
auto [cost, u] = cp;
for (const auto& edge : adj_list[u]) {
Cost new_cost = cost + edge.cost; // TODO: 問題によってはここが変更の必要あり
if (new_cost < dist[edge.to]) {
dist[edge.to] = new_cost;
pq.push(make_pair(new_cost, edge.to));
}
}
}
return dist;
};/*}}}*/
vector<Cost> dijkstra(Pos start) { // 1点スタート{{{
vector<Pos> starts = {start};
return dijkstra(starts);
};/*}}}*/
};
// snippet:Graph }}}
// snippet:StronglyConnectedComponents {{{
struct StronglyConnectedComponents {
const Graph<> &g; //{{{
vector<int> comp; // comp[i]: iが属する強連結成分が何番目の成分か
Graph<> dag; // 縮約されたDAG graph. sizeをとれば強連結成分の個数が分かる。
Graph<> _rg; // reversed graph
vector<int> _order; // order[i]: 帰りがけ順
vector<int> _used;
StronglyConnectedComponents(Graph<> &_g)
: g(_g), comp(_g.n, -1), _rg(_g.n), _used(_g.n) {
for (int i = 0; i < g.n; i++) {
for (auto e : g[i]) {
_rg.add_edge(e.to, e.from, e.cost, e.idx);
}
}
build();
}
int operator[](int k) { return comp[k]; }
void build() {
for (int i = 0; i < g.n; i++) _dfs(i);
reverse(begin(_order), end(_order));
int cnt = 0;
for (int u : _order)
if (comp[u] == -1) _rdfs(u, cnt), cnt++;
dag = Graph(cnt);
for (int u = 0; u < g.n; u++) {
for (auto &e : g[u]) {
if (comp[u] == comp[e.to]) continue;
dag.add_edge(comp[u], comp[e.to]);
}
}
}
void _dfs(int idx) {
if (_used[idx]) return;
_used[idx] = true;
for (auto &e : g[idx]) _dfs(e.to);
_order.push_back(idx);
}
void _rdfs(int idx, int cnt) {
if (comp[idx] != -1) return;
comp[idx] = cnt;
for (auto e : _rg[idx]) _rdfs(e.to, cnt);
} //}}}
};
// how to use
// StronglyConnectedComponents scc(g); // g: Graph
// scc.build();
// dump(scc.comp, scc.dag.adj_list);
// snippet:StronglyConnectedComponents }}}
// snippet:topological_sort {{{
using Pos = int;
tuple<bool, vector<Pos>, int> topological_sort(const Graph<>& g) {
vector<Pos> res; // sort後の結果を格納
vector<int> h(g.n); // 頂点ごとの入次数
stack<Pos> st; // 入次数が0になっている頂点の集合
int max_len = 0; // 最長経路の長さ
// 入次数を計算する。
rep(u, g.n) {
for (const auto& edge : g[u]) {
h[edge.to]++;
}
}
// 最初に入次数0になっている頂点を集める。
rep(u, g.n) {
if (h[u] == 0) {
st.push(u);
res.push_back(u);
}
}
// 入次数0の頂点をresに追加しそこから出て行く辺は削除していく。O(g.n+E)
while (!st.empty()) {
stack<Pos> nex_st;
while (!st.empty()) {
Pos u = st.top(); st.pop();
for (const auto& edge : g[u]) {
h[edge.to]--;
if (h[edge.to] == 0) {
res.push_back(edge.to);
nex_st.push(edge.to);
}
}
}
max_len++;
st = nex_st;
}
bool is_valid = (sz(res)==g.n ? true : false);
return {is_valid, res, max_len}; // res.size()<g.nなら閉路がありDAGではない。閉路内の頂点はstに入り得ないので。
}
// snippet:topological_sort }}}
struct two_sat{
using Pos = ll;
using Size = ll;
Size orig_n;
Graph<> g;
vector<int> assigned;
two_sat(Size _orig_n): orig_n(_orig_n){
g = Graph<>(orig_n * 2); // 頂点倍加
};
Pos toid(Pos u, bool is_u) {
return u * 2 + is_u;
}
void add_condition(Pos u, bool is_u, Pos v, bool is_v) {
// add condition (u == is_u or v == is_v)
g.add_edge(toid(u, is_u^1), toid(v, is_v));
g.add_edge(toid(v, is_v^1), toid(u, is_u));
}
bool build(){
// 割当に成功したらtrue、そうでなければfalseを返す。
StronglyConnectedComponents scc(g);
auto ts = get<1>(topological_sort(scc.dag));
vec<Size> ord(sz(ts));
rep(i, sz(ts)) ord[ts[i]] = i;
// check valid
rep(u, orig_n){
if (scc.comp[toid(u, 0)] == scc.comp[toid(u, 1)]) {
return false;
}
}
assigned = vector<int>(orig_n, -1);
rep(u, orig_n){
assigned[u] = (ord[scc.comp[toid(u, 0)]] < ord[scc.comp[toid(u, 1)]] ? 1 : 0);
}
return true;
}
};
int solve() {
ll n;cin>>n;
vector<ll> s(n);
rep(i, n) { cin>>s[i]; s[i]--; }
vector<ll> t(n);
rep(i, n) { cin>>t[i]; t[i]--; }
vector<ll> u(n);
rep(i, n) { cin>>u[i]; }
auto toid = [&](int i, int j) {
return i * n + j;
};
two_sat ts(n*n);
rep(i, n)rep(j, n){
if (u[i] == 0) { ts.add_condition(toid(s[i], j), 1, toid(j, t[i]), 1); }
if (u[i] == 1) { ts.add_condition(toid(s[i], j), 0, toid(j, t[i]), 1); }
if (u[i] == 2) { ts.add_condition(toid(s[i], j), 1, toid(j, t[i]), 0); }
if (u[i] == 3) { ts.add_condition(toid(s[i], j), 0, toid(j, t[i]), 0); }
}
bool valid = ts.build();
if (!valid){
cout << -1 << endl;
return 0;
}
vvl ans(n, vl(n));
rep(i, n) {
rep(j, n){
ans[i][j] = ts.assigned[toid(i, j)];
}
rep(j, sz(ans[i])) cout << ans[i][j] << (j!=sz(ans[i])-1 ? " " : "\n");
}
return 0;
}
int main(){/*{{{*/
solve();
check_input();
return 0;
}/*}}}*/