def synthetic_data(size = 1000,n_stages = 4,n_features = 2,noise = False,size_noise = 0.1):
    data = pd.DataFrame(np.arange((int(size/n_stages))*n_stages), columns=['id'])
    data['stages'] = [0]*(int(size/n_stages))*n_stages
    start = 0
    feature_cols = []
    for stage in range(n_stages):
        ways = []
        for _ in range(np.random.randint(2,n_stages+1)):
            ways.append(np.random.randint(1,np.random.randint(2,n_stages+1)))
        ways = pd.unique(ways)
        if len(ways) == 1:
            if ways[0] == 1:
                ways = np.insert(ways,[1],[2])
            else:
                ways = np.insert(ways,[0],[1])
        data.loc[start:start+int(size/n_stages),'stages'] = data.loc[start:start+int(size/n_stages),'stages'].apply(lambda x:ways)

        start += int(size/n_stages)

    data = data.explode('stages')
    data['stages'] = data['stages'].astype(str)
    data['from'] = data.groupby(['id'])['stages'].shift(1)
    edges = data.loc[:, ['from', "stages"]].drop_duplicates().dropna().values
    edges = [list(map(str, edge)) for edge in edges]
    i = 0
    for stage in data['stages'].unique():
        transitions = list(filter(lambda x: stage in x[0], edges))
        if len(transitions) > 1:
                stage_from = stage
                stages_to = [transition[1] for transition in transitions]

                train_mask = data['from'] == stage_from
                for feat,stage_to in enumerate(stages_to):
                    mask = (data["stages"] == stage_to) & (data['from'] == stage_from)
                    data.loc[mask,'X_{}'.format(i)] = (feat + 1) + np.random.random() * 1.5
                feature_cols.append("X_{}".format(i))
        i+=1

    data[data.columns[3:]] = data[data.columns[3:]].fillna(0)
    return feature_cols,data