Background

Description

We'll say that a String is xy-balanced if for all the 'x' chars in the string, there exists a 'y' char somewhere later in the string. So "xxy" is balanced, but "xyx" is not. One 'y' can balance multiple 'x's. Return true if the given string is xy-balanced.

Format

Input

Output

Samples

aaxbby

true

aaxbb

false

yaaxbb

false

Limitation

1s, 1024KiB for each test case.