def is_simple(self):
    r"""
    EXAMPLES::

            sage: [sum(is_simple(pi) for pi in Permutations(n))  for n in range(8)]
            [1, 1, 2, 0, 2, 6, 46, 338]
    """
    n = len(self)
    if n <= 2:
        return True

    # testing intervals starting at position 0
    start = 0
    left = right = self._list[0]
    end = 1
    while end < n - 1:
        elt = self._list[end]
        if elt < left:
            left = elt
        elif elt > right:
            right = elt
        if right - left == end - start:
            return False
        elif right - left == n - 1:
            break
        end += 1

    # testing intervals starting at later positions
    for start in range(1, n - 1):
        left = right = self._list[start]
        end = start + 1
        while end < n:
            elt = self._list[end]
            if elt < left:
                left = elt
            elif elt > right:
                right = elt
            if right - left == end - start:
                return False
            elif right - left > n - 1 - start:
                break
            end += 1
            
    return True