You're causing a bRACKET!

Brian loves to code! But he can be careless at times, forgetting to put a closing brackets to his code.

Help Brian out!

Read from stdin and determine whether the brackets are "balanced" - in the sense that every opening bracket is matched by an appropriately-placed closing bracket of the same type.

Input Format
Three different types of brackets are used: round brackets (), square brackets [] and curly brackets {}.

Input will be a string containing brackets.

Constraints
Ignore characters other than brackets.

You can assume the sting contains at most 4096 characters.

Output Format
If the brackets are balanced, print Yes, balanced.

If the brackets are not balanced, print No, not balanced.

Examples

Example 0

Input: ([{}()])([]){}
Output: Yes, balanced
Explanation: All opening brackets have a matching closing bracket

Example 1

Input: ({(()([])])
Output: No, not balanced
Explanation: Each closing bracket does not have a corresponding opening bracket.

Example 2

Input: #include <stdio.h> int main (void) { printf("hello world\n"); };
Output: Yes, balanced
Explanation: Characters that are not brackets are ignored. Each opening bracket has a corresponding closing bracket.