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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException; 
import java.io.InputStream; 
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.PriorityQueue; 

class Main{ 

	static class Node{
		int c;
		long w;
		Node(int c,long w){this.c=c;this.w=w;}
	}

	static void solve(){ 
		int n = ni();
		long x = nl(), y=nl();
		mod = (long)1e9+7;
		int[] c = new int[n];
		long[] w = new long[n];
		for(int i=0;i<n;++i){
			c[i]=ni()-1;
			w[i]=nl();
		}
		long[] cTominw = new long[n];
		Arrays.fill(cTominw, Integer.MAX_VALUE);
		for(int i=0;i<n;++i){
			cTominw[c[i]]=Math.min(cTominw[c[i]], w[i]);
		}
		for(int i=0;i<n;++i)if(w[i]+cTominw[c[i]]<=x)w[i]=cTominw[c[i]];
		PriorityQueue<Node> que = new PriorityQueue<>((a,b)->a.w-b.w<0 ? -1:1);
		for(int i=0;i<n;++i)if(cTominw[i]<Integer.MAX_VALUE)que.add(new Node(i, cTominw[i]));
		Map<Integer, Integer> cton = new HashMap<>();
		int minc = que.peek().c;
		long minw = que.peek().w;
		for(int i=0;i<n;++i)if(c[i]!=minc && w[i]+minw<=y)w[i]=minw;
		que.poll();
		if(que.isEmpty()){
			out.println(1);return;
		}
		int nextc = que.peek().c;
		long nextw = que.peek().w;
		for(int i=0;i<n;++i)if(c[i]==minc && w[i]+nextw<=y)w[i]=minw;
		if(minw*2>y){
			out.println(1);return;
		}
		int all = 0;
		for(int i=0;i<n;++i)if(w[i]==minw){
			++all;
			cton.put(c[i], cton.getOrDefault(c[i], 0)+1);
		}
		fact = new long[n+1];
		fact[0]=1;
		for(int i=1;i<=n;++i)fact[i]=(fact[i-1]*i)%mod;
		inv = new long[n+1];
		for(int i=0;i<=n;++i)inv[i]=fact[i];
		for(int i=0;i<=n;++i){
			long res = 1;
			for(int j=0;j<32;++j){
				if((((mod-2)>>j)&1)==1)res=(res*inv[i])%mod;
				inv[i]=(inv[i]*inv[i])%mod;
			}
			inv[i]=res;
		}
		long ans = fact[all];
		for(int cnt: cton.values()){
			ans=(ans*inv[cnt])%mod;
		}
		out.println(ans);
	} 
	static long[] fact;
	static long[] inv;
	static long mod;
	static long comb(int n, int m){
		return ((fact[n]*inv[m]%mod)*inv[n-m])%mod;
	}
 
 
	public static void main(String[] args){ 
		 solve(); 
		 out.flush(); 
	 } 
	 private static InputStream in = System.in; 
	 private static PrintWriter out = new PrintWriter(System.out); 
 
	 private static final byte[] buffer = new byte[1<<15]; 
	 private static int ptr = 0; 
	 private static int buflen = 0; 
	 private static boolean hasNextByte(){ 
		 if(ptr<buflen)return true; 
		 ptr = 0; 
		 try{ 
			 buflen = in.read(buffer); 
		 } catch (IOException e){ 
			 e.printStackTrace(); 
		 } 
		 return buflen>0; 
	 } 
	 private static int readByte(){ if(hasNextByte()) return buffer[ptr++]; else return -1;} 
	 private static boolean isSpaceChar(int c){ return !(33<=c && c<=126);} 
	 private static int skip(){int res; while((res=readByte())!=-1 && isSpaceChar(res)); return res;} 
 
	 private static double nd(){ return Double.parseDouble(ns()); } 
	 private static char nc(){ return (char)skip(); } 
	 private static String ns(){ 
		 StringBuilder sb = new StringBuilder(); 
		 for(int b=skip();!isSpaceChar(b);b=readByte())sb.append((char)b); 
		 return sb.toString(); 
	 } 
	 private static int[] nia(int n){ 
		 int[] res = new int[n]; 
		 for(int i=0;i<n;++i)res[i]=ni(); 
		 return res; 
	 } 
	 private static long[] nla(int n){ 
		 long[] res = new long[n]; 
		 for(int i=0;i<n;++i)res[i]=nl(); 
		 return res; 
	 } 
	 private static int ni(){ 
		 int res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	 } 
	 private static long nl(){ 
		 long res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	} 
}