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: Wrong Answer)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {
	public static long MOD = 1000000007;
	public static void main(String[] args) {
		IO io = new IO();
		int n = io.nextInt();
		int x = io.nextInt();
		int y = io.nextInt();
		Ball[] b = new Ball[n];
		for(int i=0;i<n;i++) {
			int c = io.nextInt();
			int w = io.nextInt();
			b[i] = new Ball(i, c, w);
		}
		UnionFind uf = new UnionFind(n);
		Arrays.sort(b,(b1,b2)->{
			if (b1.c != b2.c) {
				return Integer.compare(b1.c, b2.c);
			}
			return Integer.compare(b1.w, b2.w);
		});
		for(int l=0;l<n;) {
			int r = l;
			while(r < n - 1 && b[r+1].c == b[l].c) {
				r++;
			}
			for(int i=l;i<=r;i++) {
				if (b[l].w + b[i].w <= x) {
					uf.union(b[l].i, b[i].i);
				}else{
					break;
				}
			}
			l = r + 1;
		}
		Arrays.sort(b,(b1,b2)->Integer.compare(b1.w, b2.w));
		for(int i=0;i<n;i++) {
			if (b[0].w + b[i].w <= y) {
				uf.union(b[0].i, b[i].i);
			}
		}
		//System.out.println(uf.groups());
		Arrays.sort(b, (b1,b2) -> Integer.compare(b1.i, b2.i));
		long[] fact = Mod.factorialArray(200010, MOD);
		long[] factInv = Mod.factorialInverseArray(200010, MOD, Mod.inverseArray(200010, MOD));
		long ans = 1;
		for(ArrayList<Integer> g: uf.groups()) {
			ArrayList<Integer> cs = new ArrayList<>();
			for(int i:g) {
				cs.add(b[i].c);
			}
			cs.sort(null);
			int m = g.size();
			long pi = fact[m];
			for(int l=0;l<m;) {
				int r = l;
				while(r < m - 1 && cs.get(r+1) == cs.get(l)) {
					r++;
				}
				pi = pi * factInv[r-l+1] % MOD;
				l = r + 1;
			}
//			System.out.println(pi);
			ans = ans * pi % MOD;
		}
		System.out.println(ans);
	}
}
class Ball {
	int i,c,w;

	public Ball(int i, int c, int w) {
		super();
		this.i = i;
		this.c = c;
		this.w = w;
	}
	
}
class Mod {
	public static long[] inverseArray(int maxN,long modP) {
		long[] inv = new long[maxN+1];
		inv[1] = 1;
		for(int i=2;i<=maxN;i++) {
			inv[i] = modP - (modP / i) * inv[(int) (modP%i)] % modP;
		}
		return inv;
	}
	public static long[] factorialArray(int maxN,long mod) {
		long[] fact = new long[maxN+1];
		fact[0] = 1 % mod;
		for(int i=1;i<=maxN;i++) {
			fact[i] = fact[i-1] * i % mod;
		}
		return fact;
	}
	public static long[] factorialInverseArray(int maxN,long modP,long[] inverseArray) {
		long[] factInv = new long[maxN+1];
		factInv[0] = 1;
		for(int i=1;i<=maxN;i++) {
			factInv[i] = factInv[i-1] * inverseArray[i] % modP;
		}
		return factInv;
	}
}
class UnionFind {
	private int[] parent;
	public UnionFind(int size) {
		parent = new int[size];
		Arrays.fill(parent, -1);
	}
	public boolean union(int x,int y) {
		x = root(x);
		y = root(y);
		if (x!=y) {
			if (parent[y] < parent[x]) {
				int tmp = y;
				y = x;
				x = tmp;
			}
			parent[x] += parent[y];
			parent[y] = x;
			return true;
		}
		return false;
	}
	public boolean isConnected(int x,int y) {
		return root(x)==root(y);
	}
	private int root(int x) {
		return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
	}
	public int size(int x) {
		return -parent[root(x)];
	}
	public ArrayList<ArrayList<Integer>> groups() {
		int n = parent.length;
		ArrayList<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>();
		HashMap<Integer,Integer> hm = new HashMap<Integer, Integer>();
		for(int i=0;i<n;i++) {
			int r = root(i);
			if (!hm.containsKey(r)) {
				hm.put(r, g.size());
				g.add(new ArrayList<Integer>());
			}
			g.get(hm.get(r)).add(i);
		}
		return g;
	}
	public String toString() {
		return Arrays.toString(parent);
	}
}

class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	
	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}