update dataset processing + add default dataset + update plotting + add computing metrics

.gitignore

@@ -1 +1,5 @@
 models/granite_tsfm
+__pycache__/
+.cache/
+.DS_Store
+*.pyc

app.py

@@ -1,8 +1,8 @@
 import io
 import zipfile
 from pathlib import Path
-from typing import List, Tuple
-
+from typing import List, Tuple, Literal, Optional
+from evaluation.metrics import get_metrics
 import gradio as gr
 import matplotlib
 
@@ -51,37 +51,183 @@ def ensure_checkpoints() -> None:
         zf.extractall(".")
 
 
-def load_timeseries(file_obj, feature_columns: List[str] | None = None) -> Tuple[pd.DataFrame, np.ndarray]:
-    """Load the uploaded file into a numeric dataframe and numpy array."""
-    path = Path(file_obj.name)
-    if path.suffix.lower() == ".npy":
+BASE_DIR = Path(__file__).resolve().parent
+SAMPLE_DATASET_DIR = BASE_DIR / "sample_datasets"
+
+LabelSource = Literal["same_file", "separate_file", "none"]
+LABEL_COLUMN_CANDIDATES = ("label", "labels")
+LABEL_SOURCE_CHOICES = {
+    "Value + label in same file": "same_file",
+    "Labels in separate file": "separate_file",
+    "No labels provided": "none",
+}
+SAMPLE_FILES: dict[str, dict[str, object]] = {
+    "Sample: Univariate SED Medical": {
+        "path": SAMPLE_DATASET_DIR / "235_SED_id_2_Medical_tr_2499_1st_3840.csv",
+        "is_multivariate": False,
+    },
+    "Sample: Univariate UCR Sensor": {
+        "path": SAMPLE_DATASET_DIR / "364_UCR_id_62_Sensor_tr_2833_1st_5988.csv",
+        "is_multivariate": False,
+    },
+    "Sample: Univariate Yahoo WebService": {
+        "path": SAMPLE_DATASET_DIR / "686_YAHOO_id_136_WebService_tr_500_1st_755.csv",
+        "is_multivariate": False,
+    },
+    # "Sample: Multivariate MSL Sensor": {
+    #     "path": SAMPLE_DATASET_DIR / "003_MSL_id_2_Sensor_tr_883_1st_1238.csv",
+    #     "is_multivariate": True,
+    # },
+}
+
+
+def _resolve_path(file_obj) -> Path:
+    """Extract a pathlib.Path from the gradio file object."""
+    if file_obj is None:
+        raise ValueError("File object is None.")
+
+    if isinstance(file_obj, Path):
+        return file_obj
+
+    if isinstance(file_obj, str):
+        path = Path(file_obj)
+        if not path.is_absolute():
+            path = (BASE_DIR / path).resolve()
+        return path
+
+    # Gradio may pass dictionaries or objects with a 'name' attribute.
+    if isinstance(file_obj, dict) and "name" in file_obj:
+        return _resolve_path(file_obj["name"])
+
+    name = getattr(file_obj, "name", None)
+    if not name:
+        raise ValueError("Unable to resolve uploaded file path.")
+    return _resolve_path(name)
+
+
+def _load_dataframe(path: Path) -> pd.DataFrame:
+    """Load a dataframe from supported file types."""
+    if not path.exists():
+        raise ValueError(f"File not found: {path}. If this is a bundled sample, ensure it exists under {SAMPLE_DATASET_DIR}.")
+
+    suffix = path.suffix.lower()
+    if suffix == ".npy":
         data = np.load(path, allow_pickle=False)
         if data.ndim == 1:
             data = data.reshape(-1, 1)
         if not isinstance(data, np.ndarray):
-            raise ValueError("Loaded data is not a numpy array.")
-        df = pd.DataFrame(data)
-        return df, data.astype(np.float32)
+            raise ValueError("Loaded .npy data is not a numpy array.")
+        return pd.DataFrame(data)
 
-    if path.suffix.lower() not in {".csv", ".txt"}:
+    if suffix not in {".csv", ".txt"}:
         raise ValueError("Unsupported file type. Please upload a .csv, .txt, or .npy file.")
 
-    df = pd.read_csv(path)
+    return pd.read_csv(path)
+
+
+def _extract_label_column(df: pd.DataFrame) -> Tuple[pd.DataFrame, Optional[pd.Series]]:
+    """Split a label column from dataframe if one of the candidate names exists."""
+    lower_to_original = {col.lower(): col for col in df.columns}
+    label_col = None
+    for candidate in LABEL_COLUMN_CANDIDATES:
+        if candidate in lower_to_original:
+            label_col = lower_to_original[candidate]
+            break
+
+    if label_col is None:
+        return df, None
+
+    label_series = pd.to_numeric(df[label_col], errors="raise")
+    feature_df = df.drop(columns=[label_col])
+    return feature_df, label_series
+
+
+def _load_label_series(file_obj) -> pd.Series:
+    """Load labels from a dedicated upload."""
+    path = _resolve_path(file_obj)
+    df = _load_dataframe(path)
     numeric_df = df.select_dtypes(include=np.number)
     if numeric_df.empty:
-        raise ValueError("No numeric columns detected. Ensure your file contains numeric values.")
+        raise ValueError("Uploaded label file does not contain numeric columns.")
+
+    lower_to_original = {col.lower(): col for col in numeric_df.columns}
+    for candidate in LABEL_COLUMN_CANDIDATES:
+        if candidate in lower_to_original:
+            column = lower_to_original[candidate]
+            return pd.to_numeric(numeric_df[column], errors="raise").rename("label")
+
+    if numeric_df.shape[1] > 1:
+        raise ValueError(
+            "Label file must contain exactly one numeric column or include a column named 'label'."
+        )
+
+    series = pd.to_numeric(numeric_df.iloc[:, 0], errors="raise").rename("label")
+    return series
+
+
+def load_timeseries(
+    value_file,
+    feature_columns: List[str] | None,
+    label_source: LabelSource,
+    label_file=None,
+) -> Tuple[pd.DataFrame, np.ndarray, Optional[pd.Series]]:
+    """Load the uploaded value file, optional label file, and return features/labels."""
+    value_path = _resolve_path(value_file)
+    raw_df = _load_dataframe(value_path)
+    feature_df = raw_df.select_dtypes(include=np.number)
+
+    if feature_df.empty:
+        raise ValueError("No numeric columns detected. Ensure your value file contains numeric values.")
+
+    label_series: Optional[pd.Series] = None
+    feature_df, embedded_label = _extract_label_column(feature_df)
+
+    if label_source == "same_file":
+        if embedded_label is None:
+            raise ValueError(
+                "Label column not found in the uploaded file. Expected a column named 'label'."
+            )
+        label_series = embedded_label
+    elif label_source == "separate_file":
+        if label_file is None:
+            raise ValueError("Please upload a label file or switch the label source option.")
+        label_series = _load_label_series(label_file)
+    elif label_source == "none":
+        label_series = None
+    else:
+        raise ValueError(f"Unsupported label source option: {label_source}")
 
     if feature_columns:
-        missing = [col for col in feature_columns if col not in numeric_df.columns]
+        missing = [col for col in feature_columns if col not in feature_df.columns]
         if missing:
-            raise ValueError(f"Selected columns not found in the file: {', '.join(missing)}")
-        numeric_df = numeric_df[feature_columns]
+            raise ValueError(f"Selected columns not found in the value file: {', '.join(missing)}")
+        feature_df = feature_df[feature_columns]
+
+    feature_df = feature_df.reset_index(drop=True)
+
+    if label_series is not None:
+        label_series = label_series.reset_index(drop=True)
+        if len(label_series) != len(feature_df):
+            min_length = min(len(label_series), len(feature_df))
+            label_series = label_series.iloc[:min_length].reset_index(drop=True)
+            feature_df = feature_df.iloc[:min_length, :].reset_index(drop=True)
 
-    array = numeric_df.to_numpy(dtype=np.float32)
+    array = feature_df.to_numpy(dtype=np.float32)
     if array.ndim == 1:
         array = array.reshape(-1, 1)
 
-    return numeric_df, array
+    return feature_df, array, label_series
+
+
+def _metrics_to_dataframe(metrics: dict[str, float]) -> pd.DataFrame:
+    if not metrics:
+        return pd.DataFrame({"Metric": [], "Value": []})
+    return pd.DataFrame(
+        {
+            "Metric": list(metrics.keys()),
+            "Value": [round(float(value), 4) for value in metrics.values()],
+        }
+    )
 
 
 def infer(
@@ -89,19 +235,32 @@ def infer(
     is_multivariate: bool,
     window_size: int,
     batch_size: int,
-    mask_type: str,
     multi_size: str,
     feature_columns: List[str],
-) -> Tuple[str, pd.DataFrame, plt.Figure]:
+    label_source: LabelSource,
+    label_file,
+) -> Tuple[str, pd.DataFrame, plt.Figure, pd.DataFrame]:
     """Run Time-RCD inference and produce outputs for the Gradio UI."""
     ensure_checkpoints()
-    numeric_df, array = load_timeseries(file_obj, feature_columns or None)
+    numeric_df, array, labels = load_timeseries(
+        file_obj, feature_columns or None, label_source=label_source, label_file=label_file
+    )
+
+    num_features = array.shape[1] if array.ndim > 1 else 1
+    if is_multivariate and num_features == 1:
+        raise ValueError(
+            "Dataset check: only one feature column found, so please switch the Data type to 'Univariate' or upload a multivariate file with multiple feature columns."
+        )
+    if not is_multivariate and num_features > 1:
+        raise ValueError(
+            "Dataset check: multiple feature columns detected, so please switch the Data type to 'Multivariate' or provide a univariate file with a single feature column."
+        )
 
     kwargs = {
         "Multi": is_multivariate,
         "win_size": window_size,
         "batch_size": batch_size,
-        "random_mask": mask_type,
+        "random_mask": "random_mask",
         "size": multi_size,
         "device": "cpu",
     }
@@ -111,41 +270,90 @@ def infer(
     logit_vector = np.asarray(logits).reshape(-1)
 
     valid_length = min(len(score_vector), len(numeric_df))
-    score_series = pd.Series(score_vector[:valid_length], index=numeric_df.index[:valid_length], name="anomaly_score")
-    logit_series = pd.Series(logit_vector[:valid_length], index=numeric_df.index[:valid_length], name="anomaly_logit")
+    if labels is not None:
+        valid_length = min(valid_length, len(labels))
 
     result_df = numeric_df.iloc[:valid_length, :].copy()
+    score_series = pd.Series(score_vector[:valid_length], index=result_df.index, name="anomaly_score")
+    logit_series = pd.Series(logit_vector[:valid_length], index=result_df.index, name="anomaly_logit")
     result_df["anomaly_score"] = score_series
     result_df["anomaly_logit"] = logit_series
 
+    metrics_df: pd.DataFrame
+    if labels is not None:
+        label_series = labels.iloc[:valid_length]
+        result_df["label"] = label_series.to_numpy()
+        metrics = get_metrics(score_series.to_numpy(), label_series.to_numpy())
+        metrics_df = _metrics_to_dataframe(metrics)
+    else:
+        metrics_df = pd.DataFrame({"Metric": ["Info"], "Value": ["Labels not provided; metrics skipped."]})
+
     top_indices = score_series.nlargest(5).index.tolist()
     highlight_message = (
         "Top anomaly indices (by score): " + ", ".join(str(idx) for idx in top_indices)
         if len(top_indices) > 0
         else "No anomalies detected."
     )
+    if labels is None:
+        highlight_message += " Metrics skipped due to missing labels."
 
     figure = build_plot(result_df)
 
-    return highlight_message, result_df, figure
+    return highlight_message, result_df, figure, metrics_df
 
 
 def build_plot(result_df: pd.DataFrame) -> plt.Figure:
     """Create a matplotlib plot of the first feature vs. anomaly score."""
     fig, ax_primary = plt.subplots(figsize=(10, 4))
     index = result_df.index
-    feature_cols = [col for col in result_df.columns if col not in {"anomaly_score", "anomaly_logit"}]
+    feature_cols = [
+        col for col in result_df.columns if col not in {"anomaly_score", "anomaly_logit", "label"}
+    ]
 
     primary_col = feature_cols[0]
-    ax_primary.plot(index, result_df[primary_col], label=f"{primary_col}", color="#1f77b4", linewidth=1.0)
+    ax_primary.plot(
+        index,
+        result_df[primary_col],
+        label=f"{primary_col}",
+        color="#1f77b4",
+        linewidth=1.0,
+    )
+
+    if "label" in result_df.columns:
+        anomalies = result_df[result_df["label"] > 0]
+        if not anomalies.empty:
+            ax_primary.scatter(
+                anomalies.index,
+                anomalies[primary_col],
+                label="Label = 1",
+                color="#ff7f0e",
+                marker="o",
+                s=30,
+                alpha=0.85,
+            )
+
     ax_primary.set_xlabel("Index")
     ax_primary.set_ylabel("Value")
     ax_primary.grid(alpha=0.2)
 
     ax_secondary = ax_primary.twinx()
-    ax_secondary.plot(index, result_df["anomaly_score"], label="Anomaly Score", color="#d62728", linewidth=1.0)
+    ax_secondary.plot(
+        index,
+        result_df["anomaly_score"],
+        label="Anomaly Score",
+        color="#d62728",
+        linewidth=1.0,
+    )
     ax_secondary.set_ylabel("Anomaly Score")
 
+    handles_primary, labels_primary = ax_primary.get_legend_handles_labels()
+    handles_secondary, labels_secondary = ax_secondary.get_legend_handles_labels()
+    ax_primary.legend(
+        handles_primary + handles_secondary,
+        labels_primary + labels_secondary,
+        loc="upper right",
+    )
+
     fig.tight_layout()
     return fig
 
@@ -155,27 +363,60 @@ def build_interface() -> gr.Blocks:
     with gr.Blocks(title="Time-RCD Zero-Shot Anomaly Detection") as demo:
         gr.Markdown(
             "# Time-RCD Zero-Shot Anomaly Detection\n"
-            "Upload a time series to run zero-shot anomaly detection with the pretrained Time-RCD checkpoints. "
-            "You can choose univariate or multivariate mode, adjust the window size, and configure mask settings."
+            "Start with one of the bundled datasets or upload your own time series to run zero-shot anomaly detection."
+        )
+
+        bundled_choices = list(SAMPLE_FILES.keys())
+        default_choice = bundled_choices[0] if bundled_choices else "Upload my own"
+
+        data_selector = gr.Radio(
+            choices=bundled_choices + ["Upload my own"],
+            value=default_choice,
+            label="Choose dataset",
         )
 
         with gr.Row():
-            file_input = gr.File(label="Upload time series file (.csv, .txt, .npy)", file_types=[".csv", ".txt", ".npy"])
+            file_input = gr.File(
+                label="Upload time series file (.csv, .txt, .npy)",
+                file_types=[".csv", ".txt", ".npy"],
+                visible=default_choice == "Upload my own",
+            )
+            label_source = gr.Radio(
+                choices=list(LABEL_SOURCE_CHOICES.keys()),
+                value="Value + label in same file",
+                label="Label source",
+            )
+
+        with gr.Row():
+            label_file_input = gr.File(
+                label="Upload label file (.csv, .txt, .npy)",
+                file_types=[".csv", ".txt", ".npy"],
+                visible=False,
+            )
             column_selector = gr.Textbox(
                 label="Columns to use (comma-separated, optional)",
                 placeholder="e.g. value,feature_1,feature_2",
             )
 
+        gr.Markdown(
+            "Bundled datasets live in the Downloads folder and include labels unless noted. "
+            "Select \"Upload my own\" to provide a custom file."
+        )
+
         with gr.Row():
             multivariate = gr.Radio(
                 choices=["Univariate", "Multivariate"],
-                value="Univariate",
+                value=(
+                    "Multivariate"
+                    if bundled_choices and SAMPLE_FILES[default_choice]["is_multivariate"]
+                    else "Univariate"
+                ),
                 label="Data type",
             )
             window_size_in = gr.Slider(
                 minimum=128,
-                maximum=8192,
-                value=2048,
+                maximum=20000,
+                value=15000,
                 step=128,
                 label="Window size",
             )
@@ -188,11 +429,6 @@ def build_interface() -> gr.Blocks:
             )
 
         with gr.Row():
-            mask_type_in = gr.Radio(
-                choices=["random_mask", "full_mask"],
-                value="random_mask",
-                label="Mask type (multivariate only)",
-            )
             multi_size_in = gr.Radio(
                 choices=["full", "small"],
                 value="full",
@@ -204,28 +440,74 @@ def build_interface() -> gr.Blocks:
         result_message = gr.Textbox(label="Summary", interactive=False)
         result_dataframe = gr.DataFrame(label="Anomaly Scores", interactive=False)
         plot_output = gr.Plot(label="Series vs. Anomaly Score")
-
-        def _submit(file_obj, multivariate_choice, win, batch, mask, size, columns_text):
-            if file_obj is None:
-                raise gr.Error("Please upload a time series file.")
+        metrics_output = gr.DataFrame(label="Metrics", interactive=False)
+        def _submit(
+            data_choice,
+            file_obj,
+            label_source_choice,
+            label_file_obj,
+            multivariate_choice,
+            win,
+            batch,
+            size,
+            columns_text,
+        ):
+            use_sample = data_choice != "Upload my own"
+            if use_sample:
+                sample_entry = SAMPLE_FILES[data_choice]
+                value_obj = sample_entry["path"]
+            else:
+                value_obj = file_obj
+
+            if value_obj is None:
+                raise gr.Error("Please upload a time series file or choose a sample.")
 
             feature_columns = [col.strip() for col in columns_text.split(",") if col.strip()] if columns_text else []
             is_multi = multivariate_choice == "Multivariate"
-            summary, df, fig = infer(
-                file_obj=file_obj,
+            resolved_label_source = LABEL_SOURCE_CHOICES[label_source_choice]
+            if resolved_label_source == "separate_file" and label_file_obj is None:
+                raise gr.Error("Please upload a label file or change the label source option.")
+            summary, df, fig, metrics = infer(
+                file_obj=value_obj,
                 is_multivariate=is_multi,
                 window_size=int(win),
                 batch_size=int(batch),
-                mask_type=mask,
                 multi_size=size,
                 feature_columns=feature_columns,
+                label_source=resolved_label_source,
+                label_file=label_file_obj,
             )
-            return summary, df, fig
+            return summary, df, fig, metrics
+
+        def _toggle_label_file(option):
+            return gr.update(visible=option == "Labels in separate file")
+
+        def _handle_dataset_choice(choice):
+            show_upload = choice == "Upload my own"
+            if choice == "Upload my own":
+                multi_update = gr.update()
+            else:
+                expected_multi = SAMPLE_FILES[choice]["is_multivariate"]
+                multi_update = gr.update(value="Multivariate" if expected_multi else "Univariate")
+            return gr.update(visible=show_upload), multi_update
+
+        label_source.change(fn=_toggle_label_file, inputs=label_source, outputs=label_file_input)
+        data_selector.change(fn=_handle_dataset_choice, inputs=data_selector, outputs=[file_input, multivariate])
 
         run_button.click(
             fn=_submit,
-            inputs=[file_input, multivariate, window_size_in, batch_size_in, mask_type_in, multi_size_in, column_selector],
-            outputs=[result_message, result_dataframe, plot_output],
+            inputs=[
+                data_selector,
+                file_input,
+                label_source,
+                label_file_input,
+                multivariate,
+                window_size_in,
+                batch_size_in,
+                multi_size_in,
+                column_selector,
+            ],
+            outputs=[result_message, result_dataframe, plot_output, metrics_output],
         )
 
     return demo

model_wrapper.py

@@ -450,15 +450,19 @@ def run_Time_RCD(data,  **kwargs):
             else:
                 checkpoint_path = 'checkpoints/full_mask_15_56.pth'
             config.ts_config.patch_size = 32
+        config.ts_config.num_features = data.shape[1]
     else:
         checkpoint_path = 'checkpoints/full_mask_anomaly_head_pretrain_checkpoint_best.pth'
         config.ts_config.patch_size = 16
+        config.ts_config.num_features = 1
 
     config.cuda_devices = device  # Use the device parameter properly
     print("Using CUDA device:", config.cuda_devices)
     config.win_size = win_size
     config.batch_size = batch_size
-    config.ts_config.num_features = data.shape[1]
+    # config.ts_config.num_features = data.shape[1]
+    
+    print("Here is the data shape: ", data.shape)
     print(f"Checkpoint path: {checkpoint_path}")
     cls = TimeRCDPretrainTester(checkpoint_path, config)
     score_list, logit_list = cls.zero_shot(data)

sample_datasets/686_YAHOO_id_136_WebService_tr_500_1st_755.csv

@@ -0,0 +1,1681 @@
+Data,Label
+-12.3632407773689,0
+232.13634171358,0
+430.52571793368105,0
+496.173075378765,0
+522.727572341893,0
+393.257932390811,0
+213.565994220419,0
+38.2952438682293,0
+-127.107541885994,0
+-95.03925017548109,0
+-106.601412209391,0
+-7.52539458493978,0
+32.0612030482211,0
+197.41865281019287,0
+323.040653356358,0
+336.954405258532,0
+283.577174183736,0
+130.779855457075,0
+0.9227558452515192,0
+-215.556328746695,0
+-275.877826366485,0
+-272.840852246077,0
+-249.05187224346,0
+-91.9718148835804,0
+239.831590502733,0
+382.195091834717,0
+561.899265329255,0
+630.0377180700029,0
+627.7814624379889,0
+504.893588857404,0
+365.770165469506,0
+152.214172210223,0
+85.9884860266163,0
+60.2455830227528,0
+24.8111402315968,0
+149.845019077926,0
+180.792529745664,0
+364.63274175438,0
+497.791309065616,0
+482.581536454726,0
+453.62644028571,0
+235.0701662100849,0
+61.36547444249271,0
+-35.6404221818407,0
+-140.412252601003,0
+-157.180403355837,0
+-84.67058760494001,0
+-7.33952611979112,0
+273.183262836977,0
+497.963072677309,0
+684.926149428177,0
+707.098984074987,0
+702.987212270702,0
+680.753360602258,0
+436.16093475391295,0
+240.543048080317,0
+88.771528118984,0
+-28.8520196168574,0
+64.6874582486544,0
+114.203938252107,0
+263.012912293684,0
+461.437871812817,0
+537.475008250849,0
+485.771049528955,0
+449.411584387616,0
+332.173875030068,0
+101.148815779592,0
+22.6422652576438,0
+-70.22860373068521,0
+-195.978464618681,0
+-174.999993448803,0
+76.5178672246325,0
+302.317412967712,0
+489.422605122118,0
+656.255677740785,0
+729.6760495620849,0
+706.50381080151,0
+618.2135112534829,0
+391.99961641433,0
+209.722220302298,0
+53.8268583911137,0
+14.023950602775098,0
+86.20815906588459,0
+111.19936317051,0
+188.65908628291697,0
+394.237545406156,0
+486.413013424712,0
+518.8994084129811,0
+359.135915973952,0
+301.341059835943,0
+81.7506228458875,0
+-100.368561507905,0
+-294.426057653765,0
+-156.189089943764,0
+-72.0103003301233,0
+41.379324409603,0
+262.805832790962,0
+458.61690521588,0
+642.984608160047,0
+693.154416992712,0
+664.777499974599,0
+578.814669178947,0
+388.488822793017,0
+163.98176670203898,0
+33.823164110604,0
+4.842965156470889,0
+-5.64653543941514,0
+23.9467640711378,0
+227.290988528578,0
+356.38771140502604,0
+466.849116978331,0
+380.44206229618,0
+335.46777409785705,0
+137.890365524982,0
+42.00174488615811,0
+-109.680756508003,0
+-263.445257507019,0
+-173.87051348597,0
+-130.765962050055,0
+10.037755743912,0
+291.765346128751,0
+432.0050672686151,0
+725.3180647380051,0
+689.165238620021,0
+712.419367140357,0
+680.623273551662,0
+389.1636576235,0
+188.555701339254,0
+79.2095126576895,0
+45.334835808513006,0
+154.772593524072,0
+141.067450916111,0
+305.04562182976,0
+376.834097799316,0
+506.027015720898,0
+555.094641605013,0
+463.559334293063,0
+304.784764618,0
+172.959551197435,0
+-49.79765319364671,0
+-42.6893707619453,0
+-126.442998276384,0
+3.38206845010513,0
+171.698556847743,0
+330.864252337384,0
+613.410136288909,0
+737.474981383477,0
+833.780533135298,0
+907.961509433006,0
+658.206053259314,0
+558.560271470736,0
+376.175303325165,0
+229.774653160466,0
+177.639539006839,0
+252.19150080448296,0
+297.883874321189,0
+364.49474928272105,0
+560.070325015129,0
+603.788091990035,0
+619.671893321222,0
+658.198649777604,0
+449.10113200325895,0
+320.694992970366,0
+186.38155165517887,0
+108.216963960849,0
+-10.0348351642116,0
+193.572997229745,0
+255.604811113075,0
+529.716077345118,0
+800.362703598921,0
+956.98884783606,0
+912.519033929862,0
+977.794498653076,0
+946.48250555368,0
+732.4481955118209,0
+447.377892376562,0
+435.69950497230496,0
+311.52594635605203,0
+318.324726522037,0
+482.681100942551,0
+570.855714535282,0
+675.461940038694,0
+824.436871280607,0
+835.190321535432,0
+719.265958242624,0
+599.401123911827,0
+465.75118949246496,0
+333.698097502947,0
+183.160607180414,0
+191.440624569721,0
+275.22271215935,0
+360.586053131463,0
+686.302488441446,0
+854.3862815003689,0
+1073.34835377284,0
+1071.75696687279,0
+1117.44384295249,0
+1072.2978002696,0
+864.175462372412,0
+691.269036529403,0
+493.315621809345,0
+511.827113419583,0
+538.702965186655,0
+620.763164274878,0
+803.298525957944,0
+881.0330391076379,0
+991.2211967278108,0
+1021.10574216196,0
+908.736445625107,0
+737.878022308062,0
+632.343338947952,0
+351.674635889589,0
+315.24061650748,0
+292.85208084858,0
+455.523264888422,0
+558.449095992596,0
+696.158380078962,0
+1003.72683909469,0
+1122.54484211107,0
+1266.63565811315,0
+1269.7971218922,0
+1079.47051777113,0
+976.132940684312,0
+804.642105240126,0
+548.377375119852,0
+580.500185119952,0
+530.642376837658,0
+669.024614545665,0
+759.8886026432621,0
+921.331475948741,0
+962.95836250895,0
+1029.89254789919,0
+959.337867342408,0
+699.007405449109,0
+735.167790385479,0
+475.176780895544,0
+299.279090406402,0
+354.23898714304704,0
+411.515642089868,0
+557.718772625873,0
+767.2154631260499,0
+919.781468924462,0
+1174.4537290243,0
+1206.38301766968,0
+1123.01272292485,0
+1065.2558649563,0
+934.791950969605,0
+826.631863290824,0
+601.720521916762,0
+565.460020203727,0
+506.5716457096521,0
+612.490890407173,0
+701.775502225292,0
+873.025368916297,0
+936.7458735358432,0
+946.7716725379672,0
+888.361411641707,0
+696.598992432374,0
+588.930530685997,0
+364.6841819284391,0
+308.797168704647,0
+287.633859715428,0
+398.754613388838,0
+507.959766931027,0
+793.1971909256799,0
+973.845087773513,0
+1115.34303060879,0
+1247.8953714962402,0
+1248.4533976159598,0
+1095.8814949843302,0
+885.6591402728841,0
+738.035656007224,0
+547.2302728421109,0
+490.671340893112,0
+468.525809247731,0
+534.130830469149,0
+727.6294862941361,0
+886.976625184867,0
+1019.09591409818,0
+1029.17924528058,0
+938.407010845094,0
+766.54647159659,0
+602.16389592847,0
+407.98414338695,0
+299.95504109181,0
+265.121652529649,0
+389.005463400122,0
+522.915777394844,0
+734.5494985506571,0
+1043.1227452686,0
+1039.38556098771,0
+1133.33482251116,0
+1173.51998356541,0
+1072.06333313612,0
+917.166570370295,0
+744.35077397158,0
+736.563822811395,0
+576.415334064176,0
+600.179072018099,0
+691.881433556006,0
+771.087821359525,0
+898.408984934503,0
+1001.92779584997,0
+1083.04255122087,0
+987.8473742488452,0
+755.096812943875,0
+644.012677626522,0
+483.746634530395,0
+377.305459802768,0
+344.813446459589,0
+467.481028163216,0
+655.422378720814,0
+843.4101677742681,0
+1096.21321957213,0
+1289.36897428547,0
+1410.45643358873,0
+1329.52775977257,0
+1227.56423919339,0
+1069.18892616449,0
+800.755293759977,0
+734.893544275338,0
+657.8856887415619,0
+719.4346369961951,0
+810.106682332916,0
+899.5867631817371,0
+1157.04895190508,0
+1137.97105806047,0
+1195.78280875293,0
+1089.57239317955,0
+822.0227915260319,0
+843.5900925256099,0
+603.195368427648,0
+590.4828611658529,0
+504.244294213333,0
+689.203087608678,0
+770.841851892914,0
+932.763093178187,0
+1285.55791242965,0
+1459.70924935522,0
+1492.74791566573,0
+1520.5592072365305,0
+1413.63694662493,0
+1341.20481047478,0
+973.116350720138,0
+916.063886667842,0
+804.3098238966071,0
+831.821505363429,0
+955.993862776457,0
+1148.84962336507,0
+1142.74711444195,0
+1361.76316989968,0
+1331.8030984952302,0
+1294.88423735235,0
+1158.01215443615,0
+961.520101156527,0
+808.5907055898571,0
+747.8174237465539,0
+725.767911806126,0
+739.8976793768679,0
+958.476708690012,0
+1213.04587590741,0
+1344.40308991724,0
+1663.25436727369,0
+1663.70416458094,0
+1671.32927601679,0
+1538.98851788746,0
+1440.14699062641,0
+1265.53348479814,0
+1023.87716661826,0
+984.419713108131,0
+1077.38420078108,0
+1087.16329329994,0
+1247.67324576211,0
+1410.49132730574,0
+1382.2326631575102,0
+1516.62005544642,0
+1383.04506888898,0
+1315.67914702137,0
+1071.3876833806098,0
+868.046866323248,0
+778.615940652715,0
+767.890333858069,0
+780.660676459821,0
+1097.75053309465,0
+1205.00762969423,0
+1519.17768702181,0
+1665.57135212939,0
+1734.5416338434195,0
+1639.98255683742,0
+1572.39056364703,0
+1456.05140292617,0
+1229.07089881313,0
+1088.95748379666,0
+1112.2563207054,0
+1037.50114573661,0
+1100.99959664311,0
+1286.60087999374,0
+1459.2423010518698,0
+1520.49339359586,0
+1450.22859719155,0
+1454.56332239185,0
+1240.59658274101,0
+1084.3740523231,0
+988.938340567211,0
+871.0754050555141,0
+859.985075805786,0
+876.9131226139141,0
+1106.69825498547,0
+1307.6233285029302,0
+1478.4913169111098,0
+1649.7732102143302,0
+1741.4278125591502,0
+1741.90550612271,0
+1593.45655677813,0
+1419.5902253914098,0
+1298.57000705593,0
+1119.52184010763,0
+1002.15275011595,0
+973.5738467969612,0
+1108.4835529193,0
+1225.5314372866,0
+1423.57080696801,0
+1553.7303208342098,0
+1466.25706276424,0
+1394.0185105254998,0
+1321.43865470929,0
+1083.26914705819,0
+936.948923921172,0
+785.623831302809,0
+755.894436611282,0
+848.918740953177,0
+1065.22096242629,0
+1254.42558182121,0
+1482.01559243755,0
+1634.85793234556,0
+1643.38454909949,0
+1690.6986044274202,0
+1562.47246362711,0
+1398.43832279427,0
+1176.47632758462,0
+1075.0295712534,0
+1008.52908478811,0
+1017.31274721465,0
+1152.32264526433,0
+1219.56421398243,0
+1383.9986994338,0
+1407.06622801466,0
+1415.6385485312198,0
+1453.12982870516,0
+1247.6255784103998,0
+1094.93875154745,0
+928.611512435143,0
+763.580007538024,0
+832.390394989904,0
+863.712073380573,0
+980.970712243032,0
+1256.99316078375,0
+1434.20117497302,0
+1557.2623026034305,0
+1670.1403654636902,0
+1670.6669156134,0
+1619.7641178476802,0
+1412.38404398802,0
+1258.03307558685,0
+1108.45761448913,0
+1076.91984647597,0
+1114.09081596444,0
+1111.7332050774,0
+1245.05622573784,0
+1454.30844164129,0
+1453.4304543260198,0
+1502.91012454669,0
+1496.43154957118,0
+1326.46372063423,0
+1118.71714780568,0
+1034.2642141042,0
+869.9439554915781,0
+883.0384657430161,0
+1005.43427430693,0
+1060.59742585944,0
+1343.98967033705,0
+1579.69092626337,0
+1797.9868038150198,0
+1780.34371959565,0
+1808.56427932768,0
+1694.85285178197,0
+1570.12478628447,0
+1405.32875930979,0
+1296.54581259813,0
+1204.50881043988,0
+1256.22254158635,0
+1342.19407026331,0
+1432.58489669359,0
+1530.2749034007502,0
+1680.5925229511902,0
+1659.0966919000198,0
+1650.88102248984,0
+1474.5179560537,0
+1313.20002197521,0
+1108.09286626494,0
+1009.2043225429302,0
+1103.09477835872,0
+1064.15057566225,0
+1304.76863847553,0
+1496.19219158661,0
+1743.48966700763,0
+1836.78685577698,0
+1987.95789047059,0
+1975.16058216784,0
+1944.78190961568,0
+1802.7309088698105,0
+1488.55626614835,0
+1454.64381793538,0
+1389.96033565853,0
+1395.26692094288,0
+1490.66251410738,0
+1601.40459401383,0
+1760.62607027675,0
+1811.30982134175,0
+1912.54612556219,0
+1796.5178462228,0
+1634.81208276324,0
+1458.35559308922,0
+1344.98930519182,0
+1278.6747410656,0
+1174.30000451146,0
+1309.38286843178,0
+1531.3270175461998,0
+1647.7778861440302,0
+1854.71030562432,0
+2057.69155125941,0
+2205.26287113512,0
+2233.21615042738,0
+2103.65790591758,0
+1827.38254902059,0
+1657.4586682619,0
+1506.6101362974898,0
+1565.4225591041502,0
+1413.97122400126,0
+1578.31063252558,0
+1809.67953566756,0
+1850.29010087823,0
+1945.3564363122305,0
+2023.97602282035,0
+1963.5101305204105,0
+1726.68017468772,0
+1648.41800372746,0
+1399.16620141539,0
+1371.61491627458,0
+1314.00103803829,0
+1341.79430089447,0
+1550.22752768776,0
+1769.54345896909,0
+1972.07784829953,0
+2236.9228825101,0
+2198.69003030413,0
+2218.62934401927,0
+2200.27237416703,0
+1993.76644967446,0
+1822.30473829663,0
+1610.60572439464,0
+1474.6240950923002,0
+1548.32524539547,0
+1740.97459522158,0
+1849.73497609844,0
+2080.60182977749,0
+2153.64331892634,0
+2201.78065309238,0
+2073.6829084061897,0
+1870.88504950282,0
+1544.7181818345098,0
+1431.15423251807,0
+1052.0966003779,0
+1139.1250081098,0
+1232.42041717998,0
+1500.75852253203,0
+1803.80462353164,0
+2061.2711189856,0
+2362.38407292625,0
+2553.80302999058,0
+2447.24372244343,0
+2322.8217422083803,0
+2101.15654788493,0
+1814.20746413476,0
+1418.3582905635,0
+1423.08357229651,0
+1590.96896310841,0
+1504.04209726833,0
+1672.95794344702,0
+1976.46973793839,0
+2152.41608425522,0
+2121.3839838002104,0
+1878.57956612992,0
+1791.81881183154,0
+1430.201288531,0
+1238.9949244408,0
+1051.66555818235,0
+997.493328687984,0
+1157.46644883238,0
+1466.77027401925,0
+1846.80563905943,0
+1971.6693334541696,0
+2398.2214061092104,0
+2490.90541598686,0
+2411.588073248,0
+2209.79286291778,0
+1890.2153983654896,0
+1700.46160110727,0
+1466.5317318276502,0
+1374.77835277759,0
+1437.1081595098,0
+1456.15722598586,0
+1641.40248349981,0
+1866.07769995879,0
+1954.19883475963,0
+2031.4874546587,0
+1895.20989909836,0
+1769.0425782871102,0
+1461.8811445709198,0
+1209.02621911007,0
+1013.64477677699,0
+1132.39703562188,0
+1154.10738298571,0
+1340.44647222831,0
+1653.56993330443,0
+2053.6917976121804,0
+2289.74310656483,0
+2382.81548576672,0
+2406.5753806255,0
+2318.20160938034,0
+1852.7119500332,0
+1679.68742769306,0
+1607.3246768707002,0
+1412.50115357016,0
+1493.0082530278305,0
+1562.86612971969,0
+1663.48660459759,0
+1836.1814220494896,0
+2035.91160881898,0
+2027.0751508348496,0
+1963.57097498882,0
+1795.88288144094,0
+1541.37895286678,0
+1248.85962696055,0
+1162.15221163491,0
+1133.42943211003,0
+1207.8959660589,0
+1515.63460397316,0
+1748.67853394577,0
+2099.57750160621,0
+2364.42767622882,0
+2550.57979949858,0
+2522.5561216205,0
+2243.4503765133,0
+2196.59689647906,0
+1847.36138675216,0
+1688.9279051787,0
+1681.4341270548498,0
+1515.77708051691,0
+1758.11172300646,0
+1831.1664871133896,0
+2158.1268370962,0
+2312.5768447966,0
+2396.72268532546,0
+2207.90546377642,0
+2092.36923842305,0
+1756.3516465772598,0
+1531.4141119980302,0
+1297.2146071377902,0
+1331.24970885871,0
+1397.51950176129,0
+1835.6267166600303,0
+1992.88449071686,0
+2418.7435322396,0
+2632.06253715397,0
+2621.38325627018,0
+2835.006582282,0
+2597.1216046404897,0
+2149.44272125569,0
+2108.04356378732,0
+1947.0094208604,0
+1877.20522299073,0
+1737.32402012691,0
+1995.03458393871,0
+2121.4550403888697,0
+2332.8111892198103,0
+2452.52411590408,0
+2461.73422277185,0
+2452.8321443671102,0
+2220.56440839477,0
+1953.5168009361605,0
+1650.0261786293695,0
+1604.50942777206,0
+1478.03072853096,0
+1656.82199453361,0
+1833.5079843208,0
+2199.87078423962,0
+2585.4967601973103,0
+2849.98124949779,0
+2932.49853033034,0
+2904.31030300682,0
+2766.68576174146,0
+2591.91039387583,0
+2371.86332187915,0
+2006.1857242969,0
+1945.97347301036,0
+2013.50902293728,0
+2156.21068690945,0
+2292.39481279294,0
+2487.82448360065,0
+2673.67841098239,0
+2653.8053740037303,0
+2537.66351460189,0
+2351.94367908064,0
+2182.47209508993,0
+1874.4054592533,0
+1734.05633709193,0
+1563.30466115039,0
+1775.4991542196,0
+1990.64514523034,0
+2389.84562381385,0
+2671.82837187356,0
+2967.8894158033504,0
+3063.2898062618,0
+2934.8592855985,0
+2845.2012151535805,0
+2669.9504554561604,0
+2308.04202976691,0
+2064.17882045532,0
+2034.04970840114,0
+1971.70155359349,0
+2165.53887226526,0
+2194.22157867288,0
+2610.3684747706698,0
+2673.39662831457,0
+2650.2887912273,0
+2591.0274117664103,0
+2382.7440182933,0
+2102.46520251038,0
+1830.36507119852,0
+1608.7926920615398,0
+1646.30452060484,0
+1621.7767032422305,0
+1970.45830290968,0
+2452.2861756186803,0
+2606.14387181227,0
+2878.4644451950603,0
+2921.89202544011,0
+3006.6134796931897,0
+2785.10637704992,0
+2536.44309394952,0
+2269.47359166181,0
+2070.00138373121,0
+1972.48844623286,0
+1869.83745819655,0
+3638.99031745037,1
+2404.47676720424,0
+2467.9032858569103,0
+2512.82462387129,0
+2466.46430191658,0
+2498.70780606091,0
+2296.70209509406,0
+2019.2561200856896,0
+1743.88081507338,0
+1633.82526408912,0
+1699.00027777884,0
+1681.63286480096,0
+2015.4206335223605,0
+2177.82884307124,0
+2431.9551297547,0
+2818.6287927858,0
+2906.54701496927,0
+2910.5732881030394,0
+2551.89550389962,0
+2407.88770837209,0
+2308.6853441096696,0
+1976.3500759832104,0
+1873.2118872812805,0
+1810.8188926486896,0
+1846.08237400392,0
+2166.2188036287,0
+2423.73189676499,0
+2603.20517076941,0
+2616.10527357589,0
+2421.38672428796,0
+2186.22764820702,0
+2022.77941520262,0
+1757.77204212056,0
+1577.8991032709,0
+1450.47027095752,0
+1620.31223189049,0
+1901.52999549827,0
+2114.76889805003,0
+2482.73426962424,0
+2763.29673079151,0
+2898.4306972144104,0
+2847.88392539935,0
+2691.98050564221,0
+2517.68922202504,0
+2099.35744080091,0
+2016.33207457808,0
+1849.4925685916696,0
+1881.1444923674696,0
+2122.5466564532503,0
+2169.13328596762,0
+2488.4997530114897,0
+2479.74207023054,0
+2609.60659426582,0
+2478.47629687716,0
+2288.89499358382,0
+2099.57357924814,0
+1912.59818267815,0
+1671.92969658456,0
+1523.62699920136,0
+1645.72414067904,0
+1968.3605059198603,0
+2341.12939098704,0
+2584.6176051791,0
+2896.8422815684003,0
+3035.79266331998,0
+3058.627986528269,0
+2755.89756256211,0
+2587.3153980229,0
+2332.60944359731,0
+2141.66147054052,0
+2030.0799569913104,0
+2046.21759285815,0
+2161.3515626672897,0
+2525.1017492229603,0
+2555.51148834004,0
+2792.71770319314,0
+2768.49397076282,0
+2671.98990843304,0
+2525.50627672564,0
+2250.14239571579,0
+2016.9812616550896,0
+1791.7523348184802,0
+1903.293412316389,0
+1962.53956893654,0
+2289.31680642923,0
+2477.16218922687,0
+2926.9126312874,0
+3076.88500570016,0
+3251.5325832480103,0
+3215.8145105946,0
+3143.94354712937,0
+2855.91326150839,0
+2459.73280068951,0
+2365.5925637107603,0
+2207.40935079876,0
+3870.11802383636,1
+2397.29378272823,0
+2595.85948467427,0
+2832.39450854688,0
+1421.32274340194,1
+3047.2758322045,0
+2891.3872966517897,0
+2702.69192570609,0
+2484.73239158288,0
+2200.04571236134,0
+2108.99971406412,0
+1910.55071314482,0
+2196.18157862779,0
+2420.98419436752,0
+2815.03173421599,0
+3016.82897769392,0
+3368.8913946085604,0
+3467.76167721092,0
+3394.51257383344,0
+3295.99899221078,0
+2998.353988898089,0
+2826.91553623634,0
+2556.06155476169,0
+2449.80707524126,0
+2505.44773973183,0
+2605.37538564022,0
+2860.9553885733503,0
+3136.04688349394,0
+3167.0271868025297,0
+3159.44305770671,0
+3005.29842040194,0
+2911.43625860021,0
+2495.63510161067,0
+2457.1819458235,0
+2043.7851938121896,0
+2091.29578530436,0
+2384.7998868300697,0
+2497.46587786139,0
+2793.5799662596,0
+3098.00263258864,0
+3486.76073363265,0
+3617.18590961236,0
+3476.2222639023103,0
+3382.7824732184804,0
+3190.79193555058,0
+2782.7420199988696,0
+2606.50661792312,0
+2537.0119732671697,0
+2563.03603791936,0
+2667.57509184827,0
+2690.7235158041103,0
+3126.95843338465,0
+3260.5243158585304,0
+3324.84521250254,0
+2986.91647946768,0
+2877.3833391605103,0
+2520.99231022596,0
+2339.16131410575,0
+2211.38376414714,0
+2208.86636339712,0
+2214.1935021531,0
+2425.01115758284,0
+2766.1025002528304,0
+3088.60319327948,0
+3286.66998581073,0
+3456.77601593422,0
+3461.38176765648,0
+3184.1650423792894,0
+3009.95594166096,0
+2761.3697078995697,0
+2550.3700691829104,0
+2458.279266211,0
+2488.51379337717,0
+2561.60428591456,0
+2737.37341400889,0
+3000.2190027700103,0
+3115.45007838117,0
+3119.5447588411303,0
+3017.5012849134005,0
+2884.9643260248804,0
+2520.3470796432503,0
+2240.5086280552696,0
+1998.1652058136604,0
+1990.2748995523496,0
+2163.4675956003302,0
+2438.56599138257,0
+2735.97971407153,0
+2988.08739364836,0
+3376.42674147232,0
+3403.5368750360103,0
+3394.6956041947,0
+3202.75784453906,0
+2977.28874468302,0
+2684.2934898033604,0
+2453.30850855437,0
+2477.17730619762,0
+2377.86112254383,0
+2545.54669417999,0
+2678.9798943488,0
+2878.34990566266,0
+3067.8706066038,0
+2990.81913442148,0
+3079.10320219466,0
+2663.91257457448,0
+2514.02315020854,0
+2226.45647984918,0
+2116.45500995257,0
+1858.37102638983,0
+2092.40204578757,0
+2336.1827138323897,0
+2702.18923100399,0
+2857.1085602464696,0
+3208.3871768931704,0
+3302.77813477796,0
+3307.8899815812,0
+3303.40955794764,0
+2999.23065472769,0
+2748.40385042081,0
+2531.8992483491297,0
+2351.53596382242,0
+2402.0919098529503,0
+2493.22862914635,0
+2708.89224370235,0
+2993.9057475334603,0
+3064.2540385185603,0
+3119.84347617581,0
+2934.51708478834,0
+2852.8260926495,0
+2458.9321023561497,0
+2259.39808469867,0
+2183.15136819044,0
+2232.77375180564,0
+2211.3907788106,0
+2468.0863493468105,0
+2896.3907127515504,0
+3236.88738208284,0
+3437.4623552180296,0
+3581.2938781222206,0
+3399.41925167569,0
+3259.7978709386102,0
+3165.3350097669,0
+2921.0672456266902,0
+2598.45199846915,0
+2629.89421311839,0
+2557.1985788608604,0
+2774.92786472286,0
+2956.06525175398,0
+3118.81130689073,0
+3281.4586646084304,0
+3210.2341386041303,0
+3257.75771266859,0
+2983.22034948073,0
+2797.27520232884,0
+2481.29034166242,0
+2228.5462379292603,0
+2249.87317253662,0
+2458.89165212441,0
+2728.95870579885,0
+3006.47031278044,0
+3254.1345589131897,0
+3549.4469120584704,0
+3733.3897263913705,0
+3769.422671296261,0
+3591.9721322605296,0
+3209.36142285953,0
+3178.61421685896,0
+2834.2278123907104,0
+2826.65352848009,0
+2687.06772561932,0
+2960.09927797411,0
+3188.81970745646,0
+3422.7151344900203,0
+3400.91152500914,0
+3605.93367882423,0
+3377.7245175879902,0
+3180.35217313211,0
+2908.2428990994704,0
+2749.56330012539,0
+2511.540770084,0
+2464.455286915,0
+2683.78729746152,0
+2878.5460092897,0
+3182.4329890397,0
+3604.3197426221705,0
+3796.9343064717,0
+3811.6535485256095,0
+3857.750192222629,0
+3788.92783351156,0
+3582.79560707883,0
+3291.69583094883,0
+3033.58088106021,0
+2888.6450313356395,0
+2996.71761472578,0
+3236.72445994989,0
+3199.21144779633,0
+3595.93066152064,0
+3555.11765575139,0
+3625.32877425702,0
+3516.1440980007696,0
+3327.10025405987,0
+3122.89592887512,0
+2707.59843406746,0
+2680.60306897185,0
+2717.30758226873,0
+2790.24490683117,0
+3197.47696425618,0
+3356.39279193993,0
+3627.09783833046,0
+3948.90660218019,0
+4076.90380721394,0
+4057.37973199414,0
+3848.18892784159,0
+3656.9065293468702,0
+3376.8435324879497,0
+3178.58696595612,0
+3025.45794266815,0
+3066.0286430079304,0
+3233.2460866378497,0
+3348.1556123737,0
+3418.54218534675,0
+3644.5316370534497,0
+3698.7222223455,0
+3548.4784528236896,0
+3403.48586970299,0
+3135.42942692183,0
+2743.70919593092,0
+2709.9892515419897,0
+2714.74497967793,0
+2809.44372817273,0
+3023.19750054992,0
+3260.37202805716,0
+3663.2024542017,0
+3881.27993112005,0
+4103.44504494631,0
+4000.55778922954,0
+3680.7504277320704,0
+3580.147372070829,0
+3255.8164949607103,0
+3002.37474598466,0
+2871.42409569676,0
+2993.87939687318,0
+3119.4649912559603,0
+3356.3637172329304,0
+3369.8526981045698,0
+3636.62513853065,0
+3635.63073024606,0
+3389.9011833876098,0
+3328.35138830282,0
+2982.74853563041,0
+2795.36292025746,0
+2639.24375184702,0
+2551.77775890816,0
+2668.57597668124,0
+2965.1203820075298,0
+3274.9203991368395,0
+3515.73371003799,0
+3793.67717942366,0
+3924.92162837088,0
+3909.1124207150106,0
+3679.28511814054,0
+3535.49138051928,0
+3200.77112293901,0
+2988.9100463542304,0
+2909.51922427628,0
+2852.95949845003,0
+3004.19990630394,0
+3213.44839134078,0
+3406.19611039562,0
+3647.09525642188,0
+3461.9382809248805,0
+3490.84186517849,0
+3248.9920641856897,0
+2869.13296477359,0
+2623.45547505302,0
+2566.44075266733,0
+2456.83208712566,0
+2681.82362400195,0
+2927.7567096973803,0
+3302.55801010849,0
+3517.7659048709,0
+3764.40147258904,0
+3902.8427669093103,0
+3846.72844360698,0
+3750.35700562885,0
+3464.82677106788,0
+3180.6589854579497,0
+2946.39367273142,0
+2913.27680114342,0
+2871.30704645579,0
+3051.73833331015,0
+3242.36893965982,0
+3460.9564561154903,0
+3628.75773540464,0
+3614.59174846137,0
+3606.9795759107,0
+3267.2870622213395,0
+2964.4282337138898,0
+2797.34182972479,0
+2568.0224543299696,0
+2559.81215418847,0
+2726.89116577742,0
+3096.39549917504,0
+3401.13916142535,0
+3659.3780627932106,0
+3858.81812197906,0
+4017.6367341397295,0
+4046.9375611534497,0
+3783.35373904989,0
+3596.9272484267603,0
+3340.15366891013,0
+3078.8856896785805,0
+2913.1843324188503,0
+3031.86318373661,0
+3371.9929504441698,0
+3568.129720637829,0
+3688.22308519693,0
+3744.60633450769,0
+3768.1352337436206,0
+3669.56706472804,0
+3374.5418913169,0
+3275.91938201554,0
+2971.5410948025,0
+2850.52274312193,0
+2866.9112638846195,0
+3001.81359265831,0
+3122.5823365804804,0
+3592.51573464383,0
+3821.68516783473,0
+4076.3848201984297,0
+4203.826390053529,0
+4363.568339123271,0
+4071.89490471123,0
+3729.81574887196,0
+3643.2907759367104,0
+3524.1938784203003,0
+3247.79193496552,0
+3462.4188466872,0
+3483.68835626183,0
+3663.20185517188,0
+3964.08161930937,0
+3952.3822935554704,0
+4031.63658359665,0
+3932.199087119021,0
+3736.65361932556,0
+3401.2168351330297,0
+3071.45138817424,0
+3039.6910764604304,0
+3077.7668235166902,0
+3121.2772501783,0
+3400.32988125846,0
+3628.95512113999,0
+4112.09645106685,0
+4250.83652330927,0
+4493.62358066056,0
+4462.90010208275,0
+4287.23790846661,0
+4064.39193046915,0
+3693.6281772460497,0
+3564.8854043028496,0
+3401.0773505598804,0
+3496.6482664405103,0
+3622.6199007475,0
+3802.2911952231,0
+3904.1261845579,0
+4206.707287132,0
+4111.8670556938505,0
+4143.9801785030895,0
+3882.2582880868,0
+3573.45377961898,0
+3352.39803961198,0
+3128.34888327029,0
+3142.91214607459,0
+3325.70437869662,0
+3547.8894403738104,0
+3821.95478319414,0
+4031.7462249202704,0
+4417.2326622413,0
+4522.951368750871,0
+4427.826450472629,0
+4290.66671990577,0
+4025.75673702356,0
+3900.1704029417497,0
+3609.79229214432,0
+3465.86614825237,0
+3477.29309516777,0
+3606.29948280492,0
+3833.26193277438,0
+4010.81722275524,0
+4120.28685773625,0
+4124.69482587067,0
+4073.92824337358,0
+3920.351654609529,0
+3623.56039169044,0
+3468.73077251214,0
+3159.38885345373,0
+3129.502354712,0
+3214.9553394417403,0
+3452.65810759202,0
+3845.2316231683294,0
+4233.00147268614,0
+4386.57715350929,0
+4465.59332259255,0
+4581.7812262507705,0
+4296.48922416267,0
+4082.00319163889,0
+3835.4255851359294,0
+3583.7208310720703,0
+3478.18669093981,0
+3423.00418897228,0
+3541.45074536581,0
+3794.406386108471,0
+3956.84674849124,0
+4067.6301740110207,0
+4072.20519388026,0
+3951.3549620344,0
+3860.75546617861,0
+3540.56226066219,0
+3272.42459182868,0
+3092.3846940573803,0
+3023.4990359879102,0
+3263.5168882165003,0
+3463.43849788534,0
+3662.825795162561,0
+4006.0763688013694,0
+4264.16360718556,0
+4421.62965164386,0
+4394.556441588161,0
+4111.365142475071,0
+4018.51728087744,0
+3743.49120576958,0
+3621.9078215723903,0
+3377.02930958935,0
+3394.26171207194,0
+3531.6994371703704,0
+3674.01193036069,0
+3868.30042805286,0
+4067.94244912072,0
+4059.25770012266,0
+3964.472670085229,0
+3670.60304408442,0
+3481.7278219792,0
+3262.54140057644,0
+3146.5378048596303,0
+3035.02343085476,0
+3165.9996501612604,0
+3372.89403347299,0
+3693.4199563314296,0
+4190.42664934345,0
+4176.98829517656,0
+4479.3556347217,0
+4351.006117067121,0
+4246.23303297848,0
+4096.63065134175,0
+3648.5211232065,0
+3362.9542104092,0
+3416.03762340242,0
+3475.56838836871,0
+3529.9782088790503,0
+3674.44551809146,0
+4010.0915394696494,0
+4097.135139748471,0
+4101.20654323306,0
+4023.87405501255,0
+3835.279203745272,0
+3453.6344516974104,0
+3205.68055886102,0
+3166.2046336173303,0
+3054.14420556927,0
+3301.17034584174,0
+3543.40461720526,0
+3859.1984637710298,0
+4158.451852728061,0
+4524.96805862877,0
+4531.86501685984,0
+4537.37691112722,0
+4407.87537718566,0
+4136.826681971161,0
+3854.5717022838,0
+3675.8970926785496,0
+3583.7645874334703,0
+3614.12241470316,0
+3690.9296251487103,0
+3923.84150000183,0
+4093.46786278462,0
+4270.142798967429,0
+4237.49292795229,0
+4268.33622055348,0
+3953.10460881,0
+3784.0884122771295,0
+3443.6520820097,0
+3331.73462369073,0
+3252.57353676524,0
+3420.5044260790505,0
+3669.21168248414,0
+3929.19977740096,0
+4358.5270498684495,0
+4539.13732334922,0
+4759.359608926189,0
+4726.502295844361,0
+4655.39867224098,0
+4344.687732447511,0
+4013.23918949599,0
+3883.3715208504,0
+3750.37779865086,0
+3785.16028264688,0
+3893.5839206354,0
+4223.8523292881,0
+4430.16572069024,0
+4419.89593040677,0
+4588.75747499082,0
+4403.06931888045,0
+4291.09745662305,0
+3912.030514774,0
+3713.89127002348,0
+3544.2669170819704,0
+3623.92590236306,0
+3701.54395327542,0
+3938.03377822148,0
+4293.71998325938,0
+4477.19353373539,0
+4802.27424774998,0
+4912.98662400575,0
+5059.14537552968,0
+4806.4894600761,0
+4502.79958997646,0
+4195.36215167098,0
+3996.85664839067,0
+4002.30605754088,0
+3941.35527300524,0
+4005.08611916788,0
+4306.43471438018,0
+4654.13054504082,0
+4707.7051591963,0
+4635.25845525207,0
+4671.33892380009,0
+4330.90009722371,0
+4119.27447836257,0
+3900.298066764529,0
+3660.2473933607503,0
+3594.42295270181,0
+3750.2344170195097,0
+4055.66423267286,0
+4508.89914610522,0
+4797.72894550036,0
+4900.072217810971,0
+5086.09891663095,0
+5009.68088176119,0
+4931.266946873599,0
+4650.4960513508295,0
+4313.78799639223,0
+4178.97233678863,0
+4166.994734920449,0
+4153.52131233331,0
+4192.68101511312,0
+4206.61787184131,0
+4263.42662881131,0
+4262.55310851796,0
+4279.315665957821,0
+4240.77924893753,0
+4209.991801620279,0
+4167.55628153549,0
+4114.07996893123,0
+4095.65449533248,0
+4079.38962444851,0
+4100.77490606097,0
+4146.620996307311,0
+4192.96055388352,0
+4246.784558748111,0
+4284.331042843929,0
+4303.9539626018295,0
+4292.291679953351,0
+4273.66116502714,0
+4232.41666108536,0
+4193.574563482371,0
+4139.90067900659,0
+4118.75735437305,0
+4139.5510502240295,0
+4139.00826912887,0
+4150.60062262894,0
+4201.41634575429,0
+4217.60277075639,0
+4214.40159566972,0
+4206.38871162258,0
+4187.202201070089,0
+4121.98144661376,0
+4068.05257905736,0
+4037.1592863385104,0
+4033.38937892086,0
+4045.7027229861897,0
+4083.8156694831,0
+4133.540363751429,0
+4210.251118558321,0
+4254.02943013232,0
+4261.84089482997,0
+4233.5012074401,0
+4217.538758262921,0
+4183.68719323642,0
+4138.60628938907,0
+4086.46744625312,0
+4048.31945967391,0
+4066.7513657273694,0
+4097.020712655311,0
+4119.62126930919,0
+4143.869567829821,0
+4177.6260789595,0
+4177.03085454883,0
+4154.94977521325,0
+4121.10800034426,0
+4339.89979371925,1
+4049.77844339537,0
+4009.71049154331,0
+3990.6701019543298,0
+4025.2779997873,0
+4038.77112892274,0
+4088.73942634192,0
+4165.172142385,0
+4182.433261407079,0
+4205.63110986845,0
+4204.8102767215705,0
+4168.2657475283895,0
+4135.63533114975,0
+4081.734842264671,0
+4051.627471650229,0
+4039.0572537062,0
+4023.69606939606,0
+4046.267552780712,0
+4074.29053017971,0
+4119.37470996249,0
+4154.677714159,0
+4145.14149594843,0
+4130.25589822156,0
+4076.63743094623,0
+4051.6327220342896,0
+3997.89186234794,0
+3988.44516978076,0
+3956.3965368473296,0
+4014.16379009344,0
+4039.07627056162,0
+4089.3953641039097,0
+4143.939271614289,0
+4177.21930809269,0
+4208.763844486271,0
+4182.79807558726,0
+4162.78627506892,0
+4113.86863956122,0
+4062.09724907781,0
+4033.0985860955,0
+4034.54860368883,0
+4033.9037717155297,0
+4047.62799506608,0
+4058.18691865984,0
+4112.47781149124,0
+4166.30100804355,0
+4134.6846407065605,0
+4126.57327664435,0
+4092.20285305445,0
+4036.01778387154,0
+4000.54708272706,0
+3995.42627874978,0
+3960.18944977748,0
+3717.5477775969,1
+4025.50021577584,0
+4087.1347713139294,0
+4140.874635214579,0
+4183.08629439365,0
+4215.08248067224,0
+4185.45385015959,0
+4172.4948793191,0
+4137.9421659461495,0
+4088.17251106937,0
+4051.38958292761,0
+4029.4903603493394,0
+4015.87964359933,0
+4043.79668470044,0
+4082.5949618854297,0
+4116.41608770068,0
+4138.17886915955,0
+4143.45142505095,0
+4126.00134721418,0
+4091.23857665743,0
+4053.96449111109,0
+4022.3012455964,0
+3975.378144092672,0
+3974.60307997971,0
+3992.44164887085,0
+4037.43632170158,0
+4097.82024787131,0
+4141.56354937472,0
+4166.85717537158,0
+4221.32301775061,0
+4178.84250113265,0
+4178.89308736198,0
+4125.31210853758,0
+4102.09821383872,0
+4043.63233333588,0
+4026.32762751445,0
+4032.92881357554,0
+4035.1110943213794,0
+4092.79563287543,0
+4134.483141982871,0
+4141.1090479298,0
+4146.04197982125,0
+4108.159296233371,0
+4089.9485065474896,0
+4050.51831812777,0
+4001.79241645312,0
+3967.59465792351,0
+3966.638717682221,0
+3989.741394576789,0
+4030.40642461,0
+4064.2849467639294,0
+4100.70922577233,0
+4158.85258944431,0
+4175.30319786753,0
+4160.36156902668,0
+4151.72939520729,0
+4088.373526635829,0
+4054.26658757242,0
+4005.47221896164,0
+3988.202374028661,0
+4020.73470546889,0
+4014.45922180315,0
+4049.5230491837297,0
+4068.661315396,0
+4107.343394136429,0
+4116.36917128904,0
+4084.14639230894,0
+4051.75002374246,0
+3990.75817202096,0
+3967.24269935988,0
+3916.12553509696,0
+3919.24958468169,0
+3938.64959637574,0
+4002.64166569932,0
+4015.92260390327,0
+4078.18473917878,0
+4132.0502284873,0
+4140.71804900221,0
+4130.71387624081,0
+4078.20087068222,0
+4061.4439412174,0
+3999.2451402958295,0
+4001.84688882804,0
+3938.2615068030896,0
+3955.13128149425,0
+3963.0506857119103,0
+4000.11803081048,0
+4035.33459203994,0
+4050.47341431604,0
+4053.67513280874,0
+4039.91699383178,0
+4005.79798565029,0
+3952.82016132812,0
+3910.83927308043,0
+3873.3202897416704,0
+3864.00416150508,0
+3889.5669629855,0
+3933.20514284896,0
+3958.23762016046,0
+4041.44925853739,0
+4040.8436500933694,0
+4099.13728525931,0
+4084.9050724065705,0
+4047.9850314991,0
+4001.95761049616,0
+3962.68762740545,0
+3929.73920829663,0
+3887.58018787793,0
+3907.0586457847,0
+3918.90205194039,0
+3963.51213822079,0
+3976.99235550065,0
+4011.3401653645296,0
+3972.77985848099,0
+3978.8421340660298,0
+3955.078417236261,0
+3901.00340599418,0
+3868.28408705148,0
+3848.2331459388,0
+3808.37258012565,0
+3842.99715198544,0
+3867.84118157642,0
+3935.01978724277,0
+4016.53222090262,0
+4024.81647271886,0
+4036.4575946082,0
+4033.56177438005,0
+4026.7611086594607,0
+3964.2818155505297,0
+3916.60726208604,0
+3893.07182672823,0
+3870.6813257447902,0
+3864.65399065058,0
+3897.88082641008,0
+3926.62836022481,0
+3958.48866224271,0
+3975.5580050814,0
+3993.833975889721,0
+3958.51846171138,0
+3908.58594179226,0
+3874.13087797789,0
+3825.26725921209,0
+3839.7271959791706,0
+3805.05098890962,0
+3826.81270509022,0
+3868.75445423235,0
+3924.79577334415,0
+3975.63891847029,0
+4014.32237856074,0
+4023.3269690522498,0
+4035.2894817092297,0
+4004.5274753714098,0
+3964.6920072707694,0
+3922.01557225076,0
+3874.16647319485,0
+3862.14314064895,0
+3855.0530672998,0
+3911.34282262651,0
+3923.07607703433,0
+3951.85674659224,0
+3990.26663401,0
+3980.90471724075,0
+3972.33224586779,0
+3920.64710449849,0
+3873.12198092221,0
+3849.2913803611896,0
+3816.69470896775,0
+3796.14229437698,0
+3836.69536329258,0
+3873.07314610688,0