Contest Duration: - (local time) (100 minutes) Back to Home
D - Hachi /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

19 の数字のみからなる数字列 S が与えられます。

8 の倍数を作れるかどうか判定してください。

制約

• 1 \leq |S| \leq 2 \times 10^5
• S の各文字は 19 のいずれか

入力

S


入力例 1

1234


出力例 1

Yes


入力例 2

1333


出力例 2

No


1333 をどう並べ替えても 8 の倍数を作ることはできません。

入力例 3

8


出力例 3

Yes


Score : 400 points

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