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Time limit 1000/1000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.

Problem Description

You are given a sequence of round, square and curly brackets. Determine whether it is correct or not.

Input

There is a sequence of round ('(', ')'), square ('[', ']') and curly ('{', '}') brackets in a single line of input. The length of sequence is between 1 and 255.

Output

Write YES to output if the sequence is correct, and NO otherwise.

Example

input output

([])

YES

(({)}) NO

 

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