Task

A common data leakage mistake is fitting a scaler on the combined train+test data before splitting. This leaks test-set statistics into the training process.

Given train and test feature arrays, compute:

1. std_correct: standard deviation of train features when scaler is fit only on train (ddof=0)
2. std_leaky: standard deviation of the combined train+test features (ddof=0) — what a leaky pipeline would use
3. leaks: "yes" if stdleaky != stdcorrect (i.e., test data changes the scale), else "no"

Input

• Line 1: integer n_train
• Line 2: n_train space-separated floats (training feature values)
• Line 3: integer n_test
• Line 4: n_test space-separated floats (test feature values)

Output

Three lines:

1. std_correct (10 sig figs)
2. std_leaky (10 sig figs)
3. leaks — "yes" or "no"

Example

Input

4
1.0 2.0 3.0 4.0
2
10.0 20.0

Output

1.118033989
6.624868971
yes

Notes

• Track A: pure Python / NumPy only — no scipy, no sklearn.
• Use population standard deviation (ddof=0) throughout.
• Two std values are equal when their absolute difference is less than 1e-9.

Scaffolding

def pipeline_check(train: list[float], test: list[float]) -> tuple[float, float, str]:
    """
    Returns (std_correct, std_leaky, leaks) where:
      std_correct — std of train only
      std_leaky   — std of train+test combined
      leaks       — "yes" if they differ, else "no"
    """
    pass