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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Solve{
    static public int mod = 1000000007;
    static public string al = "abcdefghijklmnopqrstuvwxyz";
    public static void Main(){
        // 方針
        //
        var nn = inta();
        var n = nn[0];
        var same = nn[1];
        var diff = nn[2];
        var minweight = new int[2,2];
        var color = new int[n];
        var weight = new int[n];
        for(int i=0;i<n;i++){
            var a = inta();
            color[i] = a[0];
            weight[i] = a[1];
            if(minweight[0,0] == 0){
                minweight[0,0] = a[0];
                minweight[0,1] = a[1];
            }else if(minweight[1,0] == 0 && minweight[0,0] != a[0]){
                minweight[1,0] = a[0];
                minweight[1,1] = a[1];
            }else{
                if(a[1] < minweight[0,1]){
                    if(a[0] == minweight[0,0]){
                        minweight[0,1] = a[1];
                    }else{
                        minweight[1,0] = minweight[0,0];
                        minweight[1,1] = minweight[0,1];
                        minweight[0,0] = a[0];
                        minweight[0,1] = a[1];
                    }
                }else{
                    if(a[0] == minweight[0,0]) continue;
                    if(a[1] < minweight[1,1]){
                        if(a[0] == minweight[1,0]){
                            minweight[1,1] = a[1];
                        }else{
                            minweight[1,0] = a[0];
                            minweight[1,1] = a[1];
                        }
                    }
                }
            }
        }
        
        var samecolorchecker = true;
        for(int i=0;i<n-1;i++){
            if(color[i] != color[i+1]) samecolorchecker = false;
        }
        if(samecolorchecker){
            WriteLine(1);
            return;
        }
        
        Array.Sort(color,weight);
        /*
        WriteLine(string.Join(" ",color));
        WriteLine(string.Join(" ",weight));
        WriteLine($"{minweight[0,0]} {minweight[0,1]}");
        WriteLine($"{minweight[1,0]} {minweight[1,1]}");
        */
        var now = color[0];
        var total = 0;
        var divlist = new List<long>();
        for(int i=0;i<n;i++){
            var list = new List<int>();
            if(i == n-1 && color[i] != color[i-1]){
                if((color[i] != minweight[0,0] && weight[i] + minweight[0,1] <= diff) || (color[i] != minweight[1,0] && weight[i] + minweight[1,1] <= diff)) total++;
                break;
            }
            while(color[i] == color[i+1]){
                list.Add(weight[i]);
                i++;
                if(i == n-1) break;
            }
            list.Add(weight[i]);
            list.Sort();
            //WriteLine(string.Join(" ",list));
            var checker = false;
            if(color[i] != minweight[0,0] && list[0] + minweight[0,1] <= diff) checker = true;
            if(!checker && color[i] != minweight[1,0] && list[0] + minweight[0,1] <= diff) checker = true;
            if(!checker) continue;
            var c = 1;
            for(int j=1;j<list.Count;j++){
                if(list[0]+list[j] <= same) c++;
            }
            total += c;
            divlist.Add(c);
        }
        divlist.RemoveAll(k => k==1);
        //WriteLine(total);
        //WriteLine(string.Join(" ",divlist));
        long ans = 1;
        for(int i=total;i>=2;i--){
            long temp = i;
            ans *= temp;
            try{
                if(ans % divlist[0] == 0){
                    ans /= divlist[0];
                    divlist[0]--;
                    if(divlist[0] == 1) divlist.RemoveAt(0);
                }
            }catch{
                ans %= mod;
            }
        }
        WriteLine(ans);
        
	
	
    }
    public static void swap(ref int a,ref int b){int temp = a;a= b;b = temp;}
    static void charswap(ref char a,ref char b){char temp = a;a= b;b = temp;}
    static int ncr(int n,int r){if(n<r)return 0;r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    static int square2(int a,int b){long output = 1;var list = new List<long>();int sh = 1;long n = a;list.Add(a);while(sh < b){sh *= 2;n = n*n%mod;list.Add(n);}for(int i=list.Count-1;i>=0;i--){if(b > sh){b -= sh;sh /= 2;output = output*list[i]%mod;}}return (int)output;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static char[] chara(){ string[] a=stra();string b="";for(int i=0;i<a.Length;i++){b+=a[i];}return b.ToCharArray();}
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
    static void WriteArray(int[,] a,int b,int c){for(int i=0;i<b;i++){for(int j=0;j<c;j++){if(j!=0) Write(" ");Write(a[i,j]);}WriteLine();}}
}