Problem:
Score : 1000 points

Problem Statement

Snuke arranged N colorful balls in a row.
The i-th ball from the left has color c_i and weight w_i.

He can rearrange the balls by performing the following two operations any number of times, in any order:

Operation 1: Select two balls with the same color. If the total weight of these balls is at most X, swap the positions of these balls.

Operation 2: Select two balls with different colors. If the total weight of these balls is at most Y, swap the positions of these balls.

How many different sequences of colors of balls can be obtained? Find the count modulo 10^9 + 7.

Constraints

1 ≤ N ≤ 2 × 10^5

1 ≤ X, Y ≤ 10^9

1 ≤ c_i ≤ N

1 ≤ w_i ≤ 10^9

X, Y, c_i, w_i are all integers.

Input

Input is given from Standard Input in the following format:

N X Y
c_1 w_1
:
c_N w_N

Output

Print the answer.

Sample Input 1

4 7 3
3 2
4 3
2 1
4 4

Sample Output 1

2

The sequence of colors (2,4,3,4) can be obtained by swapping the positions of the first and third balls by operation 2.

It is also possible to swap the positions of the second and fourth balls by operation 1, but it does not affect the sequence of colors.

Sample Input 2

1 1 1
1 1

Sample Output 2

1

Sample Input 3

21 77 68
16 73
16 99
19 66
2 87
2 16
7 17
10 36
10 68
2 38
10 74
13 55
21 21
3 7
12 41
13 88
18 6
2 12
13 87
1 9
2 27
13 15

Sample Output 3

129729600

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

//set many funcs template
//Ver.20181228
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    srand(time(0));
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

typedef struct{
long long val;
long long node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
if(((sd*)a)->node < ((sd*)b)->node){return -1;}
if(((sd*)a)->node > ((sd*)b)->node){return 1;}
return 0;
}

long long factorial[262144];

void cfact(){
    long long i;
    factorial[0]=1;
    factorial[1]=1;
    for(i=2;i<262144;i++){
        factorial[i]=factorial[i-1]*i;
        factorial[i]%=mod;
    }
}

long long power(long long a, long long b){
	long long x = 1, y = a;
	while (b > 0){
		if(b%2){
			x = (x*y)%mod;
		}
		y = (y*y)%mod;
		b /= 2;
	}
	return x%mod;
}
 
long long modular_inverse(long long n){
	return power(n, mod-2);
}

long long calcnCr(long long n,long long k){
	return (factorial[n]*(modular_inverse(factorial[k])*modular_inverse(factorial[n-k])%mod))%mod;
}

int main(void){
  cfact();
  long long i,j,n,m,k,a,b,c,h,w,r=0,l,t=llinf,x,y,bas;
  long long resa[524288]={0},rp=0;
  sd data[524288];
  scanf("%lld%lld%lld",&n,&x,&y);
  for(i=1;i<=n;i++){
    scanf("%lld%lld",&data[i].val,&data[i].node);
    t=llmin(t,data[i].node);
  }
  qsort(&data[1],n,sizeof(data[1]),sdsortfnc);
  data[0].val=-llinf;
  data[n+1].val=llinf;
  for(i=1;i<=n+1;i++){
    if(data[i].val!=data[i-1].val){
      bas=i;
      if(resa[rp]!=0){rp++;}
      if(i==n+1){break;}
      if(t+data[i].node<=y){
        resa[rp]=1;
      }
    }
    else if(resa[rp]!=0 && data[bas].node+data[i].node<=x){
      resa[rp]++;
    }
  }
  if(rp==0){
    printf("1\n");
    return 0;
  }
  w=0;
  r=1;
  for(i=0;i<rp;i++){
    w+=resa[i];
  }
  for(i=0;i<rp;i++){
    r*=calcnCr(w,resa[i]);
    r%=mod;
    w-=resa[i];
  }
  printf("%lld\n",r);
  return 0;
}