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;
typedef long long ll;
const int N = 5e2 + 20, MOD = (int)1e9+7;
ll binpow(ll a,ll b) {
ll ans = 1,k = a;
while(b) {
if(b % 2)ans *= k;
ans %= MOD;
k *= k;
k %= MOD;
b /= 2ll;
}
return ans;
}
ll bp[N];
ll mem[N][N];
ll ceis(ll n,ll k){
if(k > n) return 0;
if(n < N && mem[n][k]) return mem[n][k];
ll d = 1;
for(ll i = n - k + 1;i <= n;i++){
d = i % MOD * d % MOD;
}
for(ll i = 2;i <= k;i++){
d = d * bp[i]%MOD;
}
if(n < N){
mem[n][k] = d;
}
return d;
}
int n;
array<int,2> a[N];
vector<int> b;
vector<array<int,2>> o;
ll dp[N][N],pref[N][N],c[N][N];
int m;
void test(){
cin >> n;
for(int i = 1;i <= n;i++){
cin >> a[i][0] >> a[i][1];
b.push_back(a[i][0]);
b.push_back(a[i][1] + 1);
bp[i] = binpow(i,MOD-2);
}
sort(b.begin(),b.end());
b.resize(unique(b.begin(),b.end()) - b.begin());
for(int i = 1;i < (int)b.size();i++){
o.push_back({b[i-1],b[i]-1});
// cout << b[i-1] << ' ' << b[i]-1 << '\n';
}
int m = (int)o.size();
for(int i = 0;i <= m;i++){
pref[0][i] = 1;
}
for(int i = 1;i <= m;i++){
int s = (o[i - 1][1] - o[i - 1][0]+1);
c[i][1] = s;
for(int j = 2;j <= n;j++){
for(int k = 0;k <= j-2;k++){
c[i][j] = (c[i][j] + ceis(j-2,k)*ceis(s,j-k)%MOD)%MOD;
}
}
}
// return;
for(int i = 1;i <= n;i++){
pref[i][0] = 1;
for(int j = 1;j <= m;j++){
dp[i][j] = dp[i - 1][j];
if(a[i][0] <= o[j - 1][0] && a[i][1] >= o[j-1][1]){
for(int k = i,col = 0;k >= 1;k--){
if(a[k][0] <= o[j-1][0] && a[k][1] >= o[j-1][1]){
++col;
dp[i][j] += pref[k-1][j-1]*c[j][col]%MOD;
// cout << j << ' ' << col << ' ' << c[j][col]%MOD << "x\n";
if(dp[j][j] >= MOD) dp[i][j] -= MOD;
}
}
}
}
for(int j = 1;j <= m;j++){
// cout << dp[i][j] << ' ';
pref[i][j] = (pref[i][j - 1] + dp[i][j])%MOD;
}
// cout << '\n';
}
cout << (pref[n][m]-1+MOD)%MOD << '\n';
}
int main() {
ios_base::sync_with_stdio(false);cin.tie(0);
int t = 1;
// cin >> t;
while(t--){
test();
}
}
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