M. The Journey Onwards...
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

After struggling with pouring cola in Spirit of Cola, KP got tired and decided to try something exciting: parkour.

The parkour takes place in a city called Ascent. On arrival, KP acquired a new skill called Blask Pack, which can pop himself out a certain distance by using blask packs.

In Ascent, the parkour map turns out to be a straight line with distinct $$$n$$$ footholds; the $$$i$$$-th foothold is $$$a_i$$$ meters away from KP. KP can jump out at most $$$x$$$ meters or pop out at most $$$y$$$ meters by using the skill once.

Help him determine whether it is possible to reach the furthest foothold. If it is possible, find out the minimum number of times the skill is used.

Input

The first line contains three integers $$$n, x, y$$$ $$$(1 \leq n \leq 3000, 0 \leq x, y \leq 10^6)$$$, denoting the number of footholds and the max distance KP can jump and pop.

The second line contains $$$n$$$ distinct integers $$$a_i$$$ $$$(1 \leq a_i \leq 10^6)$$$, denoting the distance between KP and the footholds.

Output

If it is possible to reach the furthest foothold, output one line containing one integer, denoting the minimum number of times the skill is used.

Otherwise, output $$$-1$$$ instead.

Examples
Input
5 6 10
3 30 15 20 6
Output
2
Input
3 4 6
1 8 12
Output
-1
Input
4 9 7
5 8 14 21
Output
0
Note

For the first sample test case, one possible way to achieve the goal is:

  1. Jump out $$$6$$$ meters to reach foothold $$$5$$$;
  2. Use skill, pop out $$$9$$$ meters to reach foothold $$$3$$$;
  3. Jump out $$$5$$$ meters to reach foothold $$$4$$$;
  4. Use skill, pop out $$$10$$$ meters to reach the furthest foothold $$$2$$$.

For the second sample test case, it is impossible to reach the furthest foothold.

For the third sample test case, note that $$$x \geq y$$$ is possible, and this makes the skill useless.

These are not the only ways to achieve the goal.