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>
using namespace std;
#define in array<int, 2>
#define pb push_back
#define pob pop_back
#define fast() ios_base::sync_with_stdio(false); cin.tie(NULL)
const int SMX = 1e6+5;
const int MX = 2e6+3;
const int LMX = 3e7+5e6;
const int mod = 1e9+7;
vector<int> g[SMX];
int lleft[LMX];
int rright[LMX];
int tree[LMX];
int nxt = 0;
int New()
{
nxt++;
lleft[nxt] = rright[nxt] = -1;
return nxt;
}
int build(int l, int r)
{
int id = New(); int m = (l+r)/2;
if(l==r)
return id;
lleft[id] = build(l, m); rright[id] = build(m+1, r); tree[id] = 0;
return id;
}
int upd(const int &i, int pos, int id, int l, int r)
{
int id_n;
if(l == r)
id_n = i;
else
id_n = New();
tree[id_n] = 1;
if(l == r)
return id_n;
lleft[id_n] = lleft[id]; rright[id_n] = rright[id];
int m = (l+r)/2;
if(pos <= m)
lleft[id_n] = upd(i, pos, lleft[id], l, m);
else
rright[id_n] = upd(i, pos, rright[id], m+1, r);
return id_n;
}
void add(const int &pp, int ql, int qr, int id, int l, int r)
{
if(qr < l || r < ql)
return;
if((ql <= l) && (r <= qr))
{
g[pp].pb(id);
return;
}
int m = (l+r)/2;
add(pp, ql, qr, lleft[id], l, m);
add(pp, ql, qr, rright[id], m+1, r);
return;
}
int pa[LMX]; bool col[LMX]; bool works = true;
int leader(int u)
{
if(pa[u] < 0)
return u;
else
{
int p = leader(pa[u]);
col[u] = col[u]^col[pa[u]];
return pa[u] = p;
}
}
void merge(int u, int v, int xr)
{
int x = leader(u);
int y = leader(v);
if(x == y)
{
if(col[u]^col[v]^xr)
works = false;
return;
}
if(pa[x] < pa[y])
{
swap(x, y);
swap(u, v);
}
pa[y]+=pa[x];
pa[x] = y;
col[x] = col[u]^col[v]^xr;
return;
}
bitset<LMX> vis, ppl;
void dfs(int u)
{
vis[u] = 1;
if(lleft[u] != -1)
{
if((!vis[lleft[u]]) && tree[lleft[u]])
dfs(lleft[u]);
if((!vis[rright[u]]) && tree[rright[u]])
dfs(rright[u]);
if(tree[lleft[u]]){
//cout << "cat_L_Calling " << lleft[u] << " from " << u << endl;
merge(u, lleft[u], 0);}
if(tree[rright[u]]){
//cout << "cat_R_Calling " << rright[u] << " from " << u << endl;
merge(u, rright[u], 0);}
return;
}
for(int v: g[u])
{
if(!tree[v])
continue;
merge(u, v, 1);
if(vis[v])
{
//cout << "Tried to call " << v << " from " << u << endl;
continue;
}
//cout << "Calling " << v << " from " << u << "\n";
dfs(v);
}
return;
}
signed main()
{
fast();//During debugging, this should ideally be removed.
int n;
cin >> n;
vector<in> vv(n);
for(int i = 0; i < n; i++)
cin >> vv[i][0] >> vv[i][1];
sort(vv.begin(), vv.end());
nxt = n; int root = build(1, 2*n); //cout << "nxt = " << nxt << endl;
for(int i = 0; i < n; i++)
{
lleft[i] = rright[i] = -1;
root = upd(i, vv[i][1], root, 1, 2*n);
add(i, vv[i][0], vv[i][1]-1, root, 1, 2*n);
//cout << "b[sn] = " << b[sn] << endl;
}
int N = nxt;
for(int i = 0; i <= N; i++)
pa[i] = -1;
for(int i = 0; i < n; i++)
dfs(i);
if(!works)
{
cout << "0\n";
return 0;
}
int ans = 1;
for(int i = 0; i < n; i++)
{
if(ppl[leader(i)])
continue;
ppl[leader(i)] = 1; ans*=2; ans%=mod;
}
cout << ans << "\n";
return 0;
}
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