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- // #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
- // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,abm,mmx,avx")
- #include <iostream>
- #include <vector>
- #include <cmath>
- #include <algorithm>
- #include <unordered_map>
- #include <set>
- #include <map>
- #include <queue>
- #include <random>
- #include <chrono>
- #define fi first
- #define se second
- #define pb push_back
- #define ll long long
- #define ld long double
- #define hm unordered_map
- #define pii pair<int, int>
- #define sz(a) (int)a.size()
- #define all(a) a.begin(), a.end()
- #define cinv(v) for (auto& x: v) cin >> x
- #define fr(i, n) for (int i = 0; i < n; ++i)
- #define fl(i, l, n) for (int i = l; i < n; ++i)
- #define int ll
- template <typename T1, typename T2> inline bool chkmin(T1 &x, const T2 &y) {if (x > y) {x = y; return 1;} return 0;}
- template <typename T1, typename T2> inline bool chkmax(T1 &x, const T2 &y) {if (x < y) {x = y; return 1;} return 0;}
- using namespace std;
- #ifdef LOCAL
- #define dbg(x) cerr << #x << " : " << x << '\n'
- #else
- #define dbg(x)
- #endif
- //tg: @runningcherry
- template <typename T1, typename T2> ostream& operator << (ostream& out, const pair<T1, T2>& v) {
- out << v.fi << ", " << v.se;
- return out;
- }
- template<typename T> ostream& operator << (ostream& out, const vector<T>& v) {
- for (auto& x: v) out << x << " ";
- return out;
- }
- template <typename T1, typename T2> istream& operator >> (istream& in, pair<T1, T2>& a) {
- in >> a.fi >> a.se;
- return in;
- }
- const ll inf = (ll) 2e9;
- const ld pi = asin (1) * 2;
- const ld eps = 1e-8;
- const ll mod = (ll)1e9 + 7;
- const ll ns = 97;
- const int maxn = 1e5 + 20;
- mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
- struct re {
- int l, r, i, c, f;
- inline bool operator < (const re& other) const {
- if (l != other.l) return l < other.l;
- return r < other.r;
- }
- };
- vector<re> edges, eb;
- vector<int> g[maxn];
- int used[maxn];
- int dfs (int v, int t, int c = inf) {
- used[v] = 1;
- if (v == t) return c;
- for (auto& u: g[v]) {
- if (!used[edges[u].r + 1] && edges[u].c - edges[u].f > 0) {
- int delta = dfs (edges[u].r + 1, min (c, edges[u].c - edges[u].f));
- if (delta > 0) {
- auto& e = edges[u];
- auto& _e = edges[u^1];
- e.f += delta;
- _e.f -= delta;
- return delta;
- }
- }
- }
- return 0;
- }
- void dfs (int v, int t, vector<int>& order) {
- if (v == t) return;
- for (auto& u: g[v]) {
- if (edges[u].c - edges[u].f > 0) {
- order.pb (edges[u].i);
- dfs (edges[u].r + 1, t, order);
- auto& e = edges[u];
- auto& _e = edges[u^1];
- e.f -= 1;
- _e.f += 1;
- return;
- }
- }
- }
- int EB = -1;
- void answer (int s, int t) {
- vector<int> order;
- dfs (s, t, order);
- vector<int> ans (sz (edges) + sz (eb));
- if (EB != -1) ans[EB] = 1;
- for (auto& x: order) {
- if (x != -1) ans[x] = 1;
- }
- cout << ans << '\n';
- exit (0);
- }
- signed main () {
- ios_base::sync_with_stdio(false);
- cin.tie(nullptr);
- cout.tie(nullptr);
- int n, m;
- cin >> n >> m;
- vector<pii> goo;
- fr (i, m) {
- int a, b;
- cin >> a >> b;
- if (a <= b) {
- fl (j, a, b + 1) g[j].pb (sz (edges));
- edges.pb ({a, b, i, 1, 0});
- fl (j, a, b + 1) g[j].pb (sz (edges));
- edges.pb ({a, b, i, 0, 0});
- }
- else eb.pb ({a, b, i, 1, 0});
- goo.pb ({a, b});
- }
- int S = n + 2, T = n + 3;
- g[S].pb (sz (edges));
- edges.pb ({0, 0, -1, 2, 0});
- g[1].pb (sz (edges));
- edges.pb ({0, n + 1, -1, 0, 0});
- g[n + 1].pb (sz (edges));
- edges.pb ({n + 1, n + 2, -1, 2, 0});
- g[T].pb (sz (edges));
- edges.pb ({0, n, -1, 0, 0});
- while (dfs (S, T)) {
- fr (i, T + 1) used[i] = 0;
- }
- int res = 0;
- for (auto& e: g[S]) res += edges[e].f;
- if (res >= 2) answer (S, T);
- g[S].pop_back ();
- g[1].pop_back ();
- g[n + 1].pop_back ();
- g[T].pop_back ();
- fr (i, 4) edges.pop_back ();
- fr (i, sz (eb)) {
- g[S].pb (sz (edges));
- edges.pb ({0, eb[i].l, -1, 1, 0});
- g[eb[i].l + 1].pb (sz (edges));
- edges.pb ({0, S - 1, -1, 0, 0});
- g[S].pb (sz (edges));
- edges.pb ({0, 0, -1, 1, 0});
- g[1].pb (sz (edges));
- edges.pb ({0, S - 1, -1, 0, 0});
- g[eb[i].r + 1].pb (sz (edges));
- edges.pb ({0, T - 1, -1, 1, 0});
- g[T].pb (sz (edges));
- edges.pb ({0, eb[i].r, -1, 0, 0});
- g[n + 1].pb (sz (edges));
- edges.pb ({0, T - 1, -1, 1, 0});
- g[T].pb (sz (edges));
- edges.pb ({0, n, -1, 0, 0});
- while (dfs (S, T)) {
- fr (i, T + 1) used[i] = 0;
- }
- res = 0;
- for (auto& e: g[S]) res += edges[e].f;
- if (res >= 2) {
- EB = eb[i].i;
- answer (S, T);
- }
- fr (i, 2) g[S].pop_back ();
- fr (i, 2) g[T].pop_back ();
- g[eb[i].l + 1].pop_back ();
- g[eb[i].r + 1].pop_back ();
- g[1].pop_back ();
- g[n + 1].pop_back ();
- fr (i, 8) edges.pop_back ();
- fr (j, sz (eb)) {
- if (i == j) continue;
- g[S].pb (sz (edges));
- edges.pb ({0, eb[i].l, -1, 1, 0});
- g[eb[i].l + 1].pb (sz (edges));
- edges.pb ({0, S - 1, -1, 0, 0});
- g[S].pb (sz (edges));
- edges.pb ({0, eb[j].l, -1, 1, 0});
- g[eb[j].l + 1].pb (sz (edges));
- edges.pb ({0, S - 1, -1, 0, 0});
- g[eb[i].r + 1].pb (sz (edges));
- edges.pb ({0, T - 1, -1, 1, 0});
- g[T].pb (sz (edges));
- edges.pb ({0, eb[i].r, -1, 0, 0});
- g[eb[j].r + 1].pb (sz (edges));
- edges.pb ({0, T - 1, -1, 1, 0});
- g[T].pb (sz (edges));
- edges.pb ({0, eb[j].r, -1, 0, 0});
- while (dfs (S, T)) {
- fr (i, T + 1) used[i] = 0;
- }
- res = 0;
- for (auto& e: g[S]) res += edges[e].f;
- if (res >= 2) {
- EB = eb[i].i;
- answer (S, T);
- }
- fr (i, 2) g[S].pop_back ();
- fr (i, 2) g[T].pop_back ();
- g[eb[i].l + 1].pop_back ();
- g[eb[i].r + 1].pop_back ();
- g[eb[j].l + 1].pop_back ();
- g[eb[j].r + 1].pop_back ();
- fr (i, 8) edges.pop_back ();
- }
- }
- cout << "impossible\n";
- }
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