Redundant Brackets

Given valid mathematical expressions in the form of a string. You are supposed to return true if the given expression contains a pair of redundant brackets, else return false. The given string only contains ‘(‘, ’)’, ‘+’, ‘-’, ‘*’, ‘/’ and lowercase English letters.

Note :

A pair of brackets is said to be redundant when a subexpression is surrounded by needless/ useless brackets.

For Example :

((a+b)) has a pair of redundant brackets. The pair of brackets on the first and last index is needless. 
While (a + (b*c)) does not have any pair of redundant brackets. 

Input Format :

The first line contains a single integer ‘T’ denoting the number of test cases. The test cases follow.

The first line of each test case contains a string denoting the expression.

Output Format :

For each test case, return “Yes” if the given expression contains at least one pair of redundant brackets, else return “No”.

Note :

You don’t need to print anything; It has already been taken care of. Just implement the given function.

Constraints :

1 <= T <= 50
3 <= |S| <= 10^4

Time Limit: 1 sec

Sample Input 1 :

2
(a+b)
(a+c*b)+(c))

Sample Output 1 :

No
Yes

Explanation of Sample Input 1 :

In the first test case, there are no redundant brackets. Hence, the output is “No”. 


In the second test case, the brackets around the alphabet ‘c’( index 8 and index 10) are redundant. Hence the output is “Yes”.

Sample Input 2 :

2
(a*b+(c/d))
((a/b))

Sample Output 2 :

No
Yes

Explanation of Sample Input 2 :

In the first test case, there are no redundant brackets. Hence, the output is “No”. 


In the second test case, the brackets around the subexpression “(a+b)” ( index 0 and index 6) are redundant. Hence the output is “Yes”.