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ZOJ Problem Set - 2725
Digital Deletions

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Digital deletions is a two-player game. The rule of the game is as following.

  • Begin by writing down a string of digits (numbers) that's as long or as short as you like. The digits can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and appear in any combinations that you like. You don't have to use them all. Here is an example:


  • On a turn a player may either:
    • Change any one of the digits to a value less than the number that it is. (No negative numbers are allowed.) For example, you could change a 5 into a 4, 3, 2, 1, or 0.
    • Erase a zero and all the digits to the right of it.

  • The player who removes the last digit wins.

  • The game that begins with the string of numbers above could proceed like this:



Now, given a initial string, try to determine can the first player win if the two players play optimally both.

Input

The input consists of several test cases. For each case, there is a string in one line.

The length of string will be in the range of [1,6]. The string contains only digit characters.

Proceed to the end of file.

Output

Output Yes in a line if the first player can win the game, otherwise output No.

Sample Input

0
00
1
20

Sample Output

Yes
Yes
No
No


Author: ZHENG, Jianqiang
Source: Zhejiang University Local Contest 2006, Preliminary
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