101813: [AtCoder]ABC181 D - Hachi

Problem Statement

Given is a digit sequence $S$ consisting of the digits from 1 through 9.

Takahashi, the bee, loves multiples of $8$.

He is trying to make a multiple of $8$ by permuting the digit sequence $S$.

Determine whether it is possible.

Constraints

• $1 \leq |S| \leq 2 \times 10^5$
• Each character of $S$ is one of the digits from 1 through 9.

Input

Input is given from Standard Input in the following format:

$S$

Output

If it is possible to make a multiple of $8$ by permuting the digit sequence $S$, print Yes; otherwise, print No.

Sample Input 1

1234

Sample Output 1

Yes

For example, permuting $1234$ into $1432$ results in a multiple of $8$.

Sample Input 2

1333

Sample Output 2

No

There is no way to permute $1333$ into a multiple of $8$.

Sample Input 3

8

Sample Output 3

Yes