Problem Description

While browsing online, Little S discovered a type of year known as a true leap year. She found that a year is considered a true leap year if it meets the following criteria:

• If a year is not a multiple of 4, it is not a true leap year.
• If a year is a multiple of 4 but not a multiple of 100, it is a true leap year.
• If a year is a multiple of 100 but not a multiple of 400, it is not a true leap year.
• If a year is a multiple of 400 but not a multiple of 3200, it is a true leap year.
• If a year is a multiple of 3200 but not a multiple of 172800, it is not a true leap year.
• If a year is a multiple of 172800, it is a true leap year.

Little S is curious about whether certain years are true leap years. Now, she will give you a year \( y \) and asks you to determine if it is a true leap year.

Input Format

A single line containing a positive integer \( y \), representing the year in question.

Output Format

A single line containing a string. If \( y \) is a true leap year, output Yes; otherwise, output No.

Sample Input and Output

Input Sample #1

2024

Output Sample #1

Yes

Input Sample #2

2100

Output Sample #2

No

Input Sample #3

2400

Output Sample #3

Yes

Input Sample #4

6400

Output Sample #5

No

Input Sample #5

518400

Output Sample #5

Yes

Notes

Sample Explanation

• \( 2024 \) meets the first rule, so it is a true leap year.
• \( 2100 \) meets the second rule, so it is not a true leap year.
• \( 2400 \) meets the third rule, so it is a true leap year.
• \( 6400 \) meets the fourth rule, so it is not a true leap year.
• \( 518400 \) meets the fifth rule, so it is a true leap year.

Data Range

For the first 30% of the data, it is guaranteed that \( y < 3200 \).
For the next 30% of the data, it is guaranteed that \( y < 172800 \).
For 100% of the data, it is guaranteed that \( 1 \leq y \leq 10^9 \).

见题面 Input 部分

见题面 Output 部分