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vector<treenode*> generate_unique_trees(int n) {
    vector<treenode*> res;
    dfs(res, 1, n);
    return res;
}

void dfs(vector<treenode*> &res, int low, int high) {
    if(low > high) {
        res.push_back(NULL);
        return;
    }
    for(int i=low; i<high; i++) {
        vector<treenode*> left_trees, right_trees;
        dfs(left_trees, low, i-1);
        dfs(right_trees, i+1, high);
        // POS1
        for(int j=0; j<left_trees.size(); j++) {
            for(int k=0; k<right_trees.size(); k++) {
                treenode *root = new treenode(i);   // gist, should be here, not at POS1
                root->left = left_trees[j];
                root->right = right_trees[k];
                res.push_back(root);
            }
        }
    }
}