Colorful Transceivers

Three people, A, B and C, are trying to communicate using transceivers. They are standing along a number line, and the coordinates of A, B and C are a, b and c (in meters), respectively. Two people can directly communicate when the distance between them is at most d meters. Determine if A and C can communicate, either directly or indirectly. Here, A and C can indirectly communicate when A and B can directly communicate and also B and C can directly communicate.

Constraints

• 1 ≤ a,b,c ≤ 100
• 1 ≤ d ≤ 100
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

a b c d

Output

If A and C can communicate, print Yes; if they cannot, print No.

Examples

Input

4 7 9 3

Output

Yes

Input

100 10 1 2

Output

No

Input

10 10 10 1

Output

Yes

Input

1 100 2 10

Output

Yes

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

a b c d

outputFormat

Output

If A and C can communicate, print Yes; if they cannot, print No.

Examples

Input

4 7 9 3

Output

Yes

Input

100 10 1 2

Output

No

Input

10 10 10 1

Output

Yes

Input

1 100 2 10

Output

Yes

样例

1 100 2 10

Yes