Vectorize a conditional sum of elements in an array of indices and another array of elements to be added

Question

I have 2 numpy array which might look like this: n = np.array([[1, 2, 2], [4, 5, 5], [7, 7, 7]]) and F = np.array([[5, 6, 7], [8, 9, 1], [2, 3, 4]])