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 int long long
using namespace std;
typedef pair<int,int> P;
const int p = 1e9 + 7;
struct UnionFind {
vector<int> root;
UnionFind(int N) {
root.resize(N);
fill(root.begin(),root.end(),-1);
}
int Find(int n) {
if(root[n]<0) return n;
int r = Find(root[n]);
root[n] = r;
return r;
}
void Merge(int x, int y) {
x = Find(x);
y = Find(y);
if(root[x]>root[y]) swap(x, y);
root[x] += root[y];
root[y] = x;
}
};
int power(int a, int b, int c) {
if(b==0) return 1;
if(b==1) return a;
if(b%2==0) {
int k = power(a, b/2, c);
return k * k % c;
}
else {
return power(a, b-1, c) * a % c;
}
}
int A[1000005];
int B[1000005];
vector<vector<int>> adj;
int dis[1000005];
bool isPos = true;
void dfs(int c, int pt) {
dis[c] = pt;
for(int n : adj[c]) {
if(dis[n]==-1) dfs(n, pt+1);
else {
if(abs(dis[n]-dis[c])%2==0) isPos = false;
}
}
}
signed main() {
cin.sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int N;
cin >> N;
int i, j;
adj.resize(N);
for(i=0;i<N;i++) cin >> A[i] >> B[i];
for(i=0;i<N;i++) dis[i] = -1;
for(i=0;i<N;i++) {
for(j=i+1;j<N;j++) {
if(A[i]<A[j]&&B[i]<B[j]&&A[j]<B[i]) {
adj[i].push_back(j);
adj[j].push_back(i);
}
if(A[i]>A[j]&&B[i]>B[j]&&B[j]>A[i]) {
adj[i].push_back(j);
adj[j].push_back(i);
}
}
}
int cnt = 0;
for(i=0;i<N;i++) {
if(dis[i]==-1) {
dfs(i, 0);
cnt++;
}
}
cout << (isPos ? power(2, cnt, p) : 0);
}
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