Non Overlapping Segments

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You are given N horizontal segments each of length R. You are given the xcoordinates of their left endpoints: the ith segment has the left end point at x_{i}. You can see that the right end point will be at x_{i} + R.
You want to move the segments such that they lie entirely in the range [0, L]. After the movements, no two segments should overlap, however, they are allowed to touch each other.
Find out the minimum number of segments that you need to move to achieve this. In other words, you want to maximize the number of segments that are left untouched. It's guaranteed that the sum of the lengths of the segments is such that they all can fit in [0, L].
Input
 The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
 The first line of each test case contains three spaceseparated integers N, L, R.
 The second line of each test case contains N spaceseparated integers. The ith integer denotes the coordinate of the left end point of ith segment, i.e. x_{i}.
Output
For each test case, output a single integer corresponding to the minimum number of segments that you need to move.
Constraints
 1 ≤ T ≤ 2500
 1 ≤ N ≤ 500
 1 ≤ L, R ≤ 10^{9}
 10^{9} ≤ x_{i} ≤ 10^{9}
 Sum of N over all test cases in a single test file won't exceed 2500.
 L ≥ R * N, i.e. all the segments can fit inside the range.
Example
Input 3 4 4 1 0 1 2 3 4 4 1 1 2 3 5 4 4 1 2 2 2 2 Output 0 2 3
Explanation
Example 1. All the segments lie in the range [0, L]. None of the segments overlap with each other. Hence, we don't need to move any segment at all.
Example 2. You can move the first segment to [0, 1]. You can also move the fourth segment to [1, 2]. After this movement, you can see that the all the segments lie in the range [0, L] and none of the segments overlap with each other. Overall, we moved 2 segments. There is no way to achieve this by moving less than 2 segments.
Author:  admin2 
Editorial  https://discuss.codechef.com/problems/NONOVSEG 
Tags  acm17kgp, admin2, dynamicprogramming, kgp17rol, medium 
Date Added:  12122017 
Time Limit:  4 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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