#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) void *wmem; char memarr[96000000]; template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } struct Modint{ unsigned val; Modint(){ } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } inline void wt_L(char a){ putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ putchar_unlocked('-'); } while(s--){ putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template int coordcomp_L(int n1, T arr1[], int n2, T arr2[], int res1[] = NULL, int res2[] = NULL, void *mem = wmem){ int i; int k = 0; pair *r; walloc1d(&r, n1+n2, &mem); for(i=(0);i<(n1);i++){ r[i].first = arr1[i]; r[i].second = i; } for(i=(0);i<(n2);i++){ r[n1+i].first = arr2[i]; r[n1+i].second = n1+i; } sort(r, r+n1+n2); for(i=(0);i<(n1+n2);i++){ if(i && r[i].first != r[i-1].first){ k++; } if(r[i].second < n1){ if(res1!=NULL){ res1[r[i].second] = k; } else{ arr1[r[i].second] = k; } } else{ if(res2!=NULL){ res2[r[i].second-n1] = k; } else{ arr2[r[i].second-n1] = k; } } } return k+1; } int N; int A[200]; int B[200]; int x[200]; int y[200]; int v[400]; int m; Modint dp[200][401]; Modint dp2[200][401]; Modint coef[201]; Modint dd[201]; Modint nn[201]; int main(){ int i, k, n; wmem = memarr; int s; int e; Modint res; Modint tmp; Modint mul; rd(N); { int Lj4PdHRW; for(Lj4PdHRW=(0);Lj4PdHRW<(N);Lj4PdHRW++){ rd(A[Lj4PdHRW]); rd(B[Lj4PdHRW]); } } for(n=(1);n<(N+1);n++){ int i, k; for(i=(0);i<(n);i++){ dd[i] = 0; } dd[n] = 1; for(k=(0);k<(n);k++){ s = n - k; nn[0] = dd[s]; for(i=(1);i<(s);i++){ nn[i] = nn[i-1] + dd[s-i]; } for(i=(0);i<(s);i++){ dd[i] = nn[i]; } } coef[n] = dd[0]; for(i=(1);i<(n+1);i++){ coef[n] /= i; } } m =coordcomp_L(N, A, N, B, x, y)- 1; for(i=(0);i<(N);i++){ v[x[i]] = A[i]; v[y[i]] = B[i]; } for(k=(0);k<(m);k++){ if(x[0] <= k && k < y[0]){ dp[0][k] = dp2[0][k] = Modint(v[k+1] - v[k]) / Modint(B[0] - A[0]); } } for(i=(1);i<(N);i++){ for(k=(0);k<(m);k++){ if(x[i] <= k && k < y[i]){ int j, z; tmp = Modint(v[k+1] - v[k]) / Modint(B[i] - A[i]); if(i%2==0){ s = k+1; e = m; } else{ s = 0; e = k; } for(j=(s);j<(e);j++){ dp[i][k] += tmp * dp[i-1][j]; } dp2[i][k] = dp[i][k]; mul = 1; for(z=(i)-1;z>=(0);z--){ if(!(x[z] <= k && k < y[z])){ break; } dp[i][k] += tmp * dp2[z][k] * coef[i-z+1] * mul; mul *= Modint(v[k+1] - v[k]) / Modint(B[z] - A[z]); } } } } res = 0; for(k=(0);k<(m);k++){ res += dp[N-1][k]; } wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20191012-1 [beta] // --- original code --- // int N, A[200], B[200]; // int x[200], y[200], v[400], m; // Modint dp[200][401], dp2[200][401]; // Modint coef[201], dd[201], nn[201]; // { // int s, e; // Modint res, tmp, mul; // rd(N,(A,B)(N)); // // rep(n,1,N+1){ // rep(i,n) dd[i] = 0; // dd[n] = 1; // rep(k,n){ // s = n - k; // nn[0] = dd[s]; // rep(i,1,s) nn[i] = nn[i-1] + dd[s-i]; // rep(i,s) dd[i] = nn[i]; // } // coef[n] = dd[0]; // rep(i,1,n+1) coef[n] /= i; // } // // // m = coordcomp(N, A, N, B, x, y) - 1; // rep(i,N) v[x[i]] = A[i], v[y[i]] = B[i]; // // rep(k,m) if(x[0] <= k < y[0]) dp[0][k] = dp2[0][k] = Modint(v[k+1] - v[k]) / Modint(B[0] - A[0]); // // // rep(i,N) wt("xy",x[i],y[i]); // // rep(i,1,N){ // // wt(i,":",dp[i-1](m)); // // wt(i,":",dp2[i-1](m)); // rep(k,m) if(x[i] <= k < y[i]){ // tmp = Modint(v[k+1] - v[k]) / Modint(B[i] - A[i]); // if(i%2==0) s = k+1, e = m; // else s = 0, e = k; // rep(j,s,e) dp[i][k] += tmp * dp[i-1][j]; // dp2[i][k] = dp[i][k]; // mul = 1; // rrep(z,i){ // if(!(x[z] <= k < y[z])) break; // dp[i][k] += tmp * dp2[z][k] * coef[i-z+1] * mul; // mul *= Modint(v[k+1] - v[k]) / Modint(B[z] - A[z]); // } // } // } // // wt(i,":",dp[i-1](m)); // // wt(i,":",dp2[i-1](m)); // // res = 0; // rep(k,m) res += dp[N-1][k]; // wt(res); // }