import copy


def FillSymmetricMatrix(matrix, N):#{{{
    """
    Fill in the bottom left part of a symmetric matrix, give the upper right
    corner filled. The input matrix is un-changed
    ------
    |+++++
    | ++++
    |  +++
    |   ++
    |    +
    """
    mtx = copy.deepcopy(matrix)
    for i in range(N):
        for j in range(i+1, N):
            mtx[j][i] = mtx[i][j]
    return mtx