def protection_aux(T, k):
    """Return the number of nodes whose minimal distance to a leaf is k
    and the minimal distance of the root to a leaf.

    """
    children = [protection_aux(t, k) for t in T]
    if len(children) == 0:
        if k == 0:
            return (1, 0)
        else:
            return (0, 0)

    kids = sum(num for num, _ in children)
    root = 1 + min(p for _, p in children)
    if root == k:
        return (1 + kids, root)
    else:
        return (kids, root)

def statistic(T):
    """Return the number of nodes whose minimal distance to a leaf is k"""
    return protection_aux(T, 1)[0]