Game with string
Description
Two people are playing a game with a string $s$, consisting of lowercase latin letters.
On a player's turn, he should choose two consecutive equal letters in the string and delete them.
For example, if the string is equal to "xaax" than there is only one possible turn: delete "aa", so the string will become "xx". A player not able to make a turn loses.
Your task is to determine which player will win if both play optimally.
The only line contains the string $s$, consisting of lowercase latin letters ($1 \leq |s| \leq 100\,000$), where $|s|$ means the length of a string $s$.
If the first player wins, print "Yes". If the second player wins, print "No".
Input
The only line contains the string $s$, consisting of lowercase latin letters ($1 \leq |s| \leq 100\,000$), where $|s|$ means the length of a string $s$.
Output
If the first player wins, print "Yes". If the second player wins, print "No".
Samples
abacaba
No
iiq
Yes
abba
No
Note
In the first example the first player is unable to make a turn, so he loses.
In the second example first player turns the string into "q", then second player is unable to move, so he loses.