Not able to build logic for problem from atcoder beginner contest

#1

Link to problem - https://atcoder.jp/contests/abc167/tasks/abc167_f

#2

Hi,

I have thought to solve this problem is that let us remove the parenthesis which are sured to get balanced. I mean to say, if the character is ( then do cnt1++ else if character is ) then if cnt1>0 then do cnt1-- else do cnt2++. I hope this much is clear. Now i sort the remaining according to cnt1-cnt2(maximum difference between no. of ( and ) brackets). Then i just check whether this is balanced or not.

#3

I did not get the last part

#4

Suppose that you have a single string having ( and ). Then initially there should be ( more than or equal to ). that is what i am telling.