Count values close to a number

Count the elements whose distance from a given number is at most D, that is |a[i] − num| ≤ D. If none qualify, print -1.

Reported in: Accenture (Aug 2022), Deloitte (memory-based)

Input

Line 1: N. Line 2: N integers. Line 3: num. Line 4: D.

Output

The count, or -1.

Constraints

1 ≤ N ≤ 10^5; 0 ≤ D.

Example 1

Input:
5
12 3 14 56 77
13
2

Output:
2

Example 2

Input:
3
1 2 3
10
1

Output:
-1

Hint: Loop once and compare abs(a[i] − num) with D.

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