vector<int> lis(vector<int> &seq) {
	int n = sz(seq), lisLength = 0, lisEnd = 0;
	vector<int> L(n), L_id(n), parents(n);
	for (int i = 0; i < n; i++) {
		int pos = upper_bound(L.begin(), L.begin() + lisLength, 
		                      seq[i]) - L.begin();
		L[pos] = seq[i];
		L_id[pos] = i;
		parents[i] = pos ? L_id[pos - 1] : -1;
		if (pos + 1 > lisLength) {
			lisLength = pos + 1;
			lisEnd = i;
	}}
	// Ab hier Rekonstruktion der Sequenz.
	vector<int> result(lisLength);
	int pos = lisLength - 1, x = lisEnd;
	while (parents[x] >= 0) {
		result[pos--] = x;
		x = parents[x];
	}
	result[0] = x;
	return result; // Liste mit Indizes einer LIS.
}