Easystackstrings

Balanced Brackets

A config parser only accepts expressions whose brackets are properly balanced. Given a string made only of the characters ( ) [ ] { }, decide whether every opening bracket is closed by the matching bracket type, in the correct order.

Input

One line containing the string s.

Output

Print YES if s is balanced, otherwise NO.

Constraints

1 ≤ |s| ≤ 10^4
s contains only ( ) [ ] { }

Sample 1

Input

{[()()]}

Output

YES

Every bracket closes in the right order.

Sample 2

Input

([)]

Output

NO

The ( is closed by ] before its own ) arrives.

Time limit 2s (3s for Python in the browser). Your code runs on your device, so timings vary a little between machines.