This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define FOR(i, x, y) for(int i = x; i < y; i++)
#define F0R(i, y) FOR(i, 0, y)
#define ROF(i, x, y) for(int i = y - 1; i >= x; i--)
#define R0F(i, y) ROF(i, 0, y)
#define WTF cout << "WTF" << endl
#define ALL(x) x.begin(), x.end()
#define RALL(x) x.rbegin(), x.rend();
#define IOS ios_base::sync_with_stdio(0); cin.tie(0)
#define F first
#define S second
#define pb push_back
using namespace std;
typedef pair<int, int> PII;
const int N = 2e6 + 7;
const int MOD = 1e9 + 7;
const int INF = 1e9 + 7;
#define lc now << 1
#define rc now << 1 | 1
int n, f[N];
int exist[N];
bool vis[N], comp[N];
PII ns[N];
PII tree[2][N << 2];
queue<int> keep;
stack<int> dr;
void change(int id, int place, PII x, int now = 1, int ls = 0, int rs = (n << 1) - 1) {
if (ls == rs) {
tree[id][now] = x;
return;
}
int mid = (ls + rs) >> 1;
if (place <= mid) change(id, place, x, lc, ls, mid);
else change(id, place, x, rc, mid + 1, rs);
if (!id) tree[0][now] = max(tree[0][lc], tree[0][rc]);
else tree[1][now] = min(tree[1][lc], tree[1][rc]);
return;
}
void init() {
cin >> n;
F0R(i, (n << 3)) tree[1][i] = {INF, INF};
F0R(i, n) {
cin >> ns[i].F >> ns[i].S;
ns[i].F--; ns[i].S--;
}
F0R(i, n) {
change(0, ns[i].F, {ns[i].S, i});
change(1, ns[i].S, {ns[i].F, i});
}
return;
}
void getEdge(int lq, int rq, int now = 1, int ls = 0, int rs = (n << 1) - 1) {
if (rq < lq || rq < ls || rs < lq) return;
if (lq <= ls && rs <= rq) {
while(1) {
PII on = tree[0][now];
if (on.F <= rq) break;
dr.push(on.S);
change(0, ns[on.S].F, {0, 0});
change(1, ns[on.S].S, {INF, INF});
}
while(1) {
PII on = tree[1][now];
if (on.F >= lq) break;
//cout << on.F << ' ' << on.S << endl;
dr.push(on.S);
change(0, ns[on.S].F, {0, 0});
change(1, ns[on.S].S, {INF, INF});
}
return;
}
int mid = (ls + rs) >> 1;
getEdge(lq, rq, lc, ls, mid);
getEdge(lq, rq, rc, mid + 1, rs);
return;
}
void bfs(int now) {
//cout << "bfs from " << now << endl;
vis[now] = 1;
comp[now] = 0;
change(0, ns[now].F, {0, 0});
change(1, ns[now].S, {INF, INF});
keep.push(now);
while(!keep.empty()) {
int on = keep.front();
keep.pop();
//cout << "get Edge for " << on << endl;
getEdge(ns[on].F, ns[on].S);
//cout << "Edges = ";
while(!dr.empty()) {
int x = dr.top(); dr.pop();
//cout << x << ' ';
comp[x] = 1 ^ comp[on];
vis[x] = 1;
keep.push(x);
}
//cout << endl;
}
return;
}
bool check() {
memset(f, 0, sizeof f);
F0R(i, n) if (!comp[i]) f[ ns[i].F ] = (i + 1), f[ ns[i].S ] = -(i + 1);
stack<int> st;
F0R(i, (n << 1)) if (f[i]) {
if (f[i] > 0) st.push(f[i]);
else {
if (st.empty() || st.top() != -f[i]) return 0;
st.pop();
}
}
memset(f, 0, sizeof f);
F0R(i, n) if (comp[i]) f[ ns[i].F ] = (i + 1), f[ ns[i].S ] = -(i + 1);
while(!st.empty()) st.pop();
F0R(i, (n << 1)) if (f[i]) {
if (f[i] > 0) st.push(f[i]);
else {
if (st.empty() || st.top() != -f[i]) return 0;
st.pop();
}
}
return 1;
}
int main() {
IOS;
init();
int ans = 1;
F0R(i, n) if (!vis[i]) {
bfs(i);
ans = (ans << 1) % MOD;
}
cout << (check() ? ans : 0);
}
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