def canonical_word(pi):
    """

    Return the word with w_i being the index of the block of i, when
    pi is sorted according to minimal elements.

    EXAMPLES:

    sage: canonical_word([[1,3],[2,4,7],[5,6]])
    1212332

    """
    pi = SetPartition(pi).standardization()
    w = [None]*pi.size()
    for i, block in enumerate(sorted([sorted(b) for b in pi]), 1):
        for e in block:
            w[e-1] = i
    return Word(w)

def statistic(pi):
    """e is internal, if there are f < e < g such that the blocks of f
    and g have larger minimal element than the block of e.

    sage: statistic([[1,4],[2,5,7],[3],[6]])
    2
    sage: canonical_word([[1,5,9,12],[2,4,8],[3,7,11],[6,10]])
    word: 123214321431
    sage: statistic([[1,5,9,12],[2,4,8],[3,7,11],[6,10]])
    5
    """
    w = canonical_word(pi)
    count = 0
    for (i, b) in enumerate(w):
        has_smaller = any(b < w[j] for j in range(i))
        has_bigger = any(b < w[j] for j in range(i+1, len(w)))
        if has_smaller and has_bigger:
            count += 1
    return count