Balanced Brackets

Statement

A string made only of the characters ( ) [ ] { } is balanced if every opening bracket is closed by the same kind of bracket in the correct order. Decide whether the given string is balanced.

Input

One line containing the string.

Output

Print YES if balanced, otherwise NO.

Constraints

1 <= length <= 200000

Example 1

([]{})

YES

Example 2

([)]

NO

The square bracket is closed while the round bracket is still open.