Lantern Chain Outer Layer Strip

A festival organizer strings several independent paper-lantern clusters into one long display cable, one cluster immediately after another with no gaps. Along the cable, each character is either ( — a new lantern shell is opened around whatever is currently open — or ) — the innermost currently open shell is sealed. The whole cable is guaranteed to be a valid sequence (every opened shell is eventually sealed, and no shell is ever sealed before it is opened), and it was built by joining, end to end, one or more self-contained clusters: a cluster never returns to zero open shells before its very last character (equivalently, no cluster can be split into two shorter clusters that are each independently valid on their own).

For a decoration touch, the organizer wants to strip away just the single outermost shell of every cluster — that cluster's very first ( and its very last ) — while keeping every other character of that cluster in its original relative order, and then splice the leftovers of all the clusters back together, in order, into one string.

Input format

• Line 1: a string s consisting only of the characters ( and ).

Output format

Print the resulting string after removing the outermost shell of every cluster (this may be an empty line if nothing is left).

Constraints

• 2 <= length of s <= 100000
• length of s is even
• s is a valid parentheses string formed by concatenating one or more primitive (self-contained) valid parentheses strings

(())(()())

()()()

((()))

(())