class Bracket107 {
	public:
	int yetanother(string s) {
		int L=s.size(),i,x,y;

		set<string> S;
		FOR(x,L) {
			string s1=s.substr(0,x)+s.substr(x+1);
			FOR(y,L) S.insert(s1.substr(0,y)+s[x]+s1.substr(y));
		}

		int ret=0;
		FORR(r,S) if(r!=s) {
			int ok=1;
			int cur=0;
			FORR(r2,r) {
				if(r2=='(') cur++;
				else cur--;
				if(cur<0) ok=0;
			}
			ret += ok;
		}
		return ret;
	}
}