Einsum double contraction in particular order causes ValueError

If I try to do

a = np.random.randn(3,3,3,3)
ans1 = np.einsum('iijj',a)

I get a ValueError:

>>> ValueError: dimensions in operand 0 for collapsing index 'j' don't match (0 != 3)

However, these alternatives work:

ans2 = np.einsum('ii', np.einsum('ijkk', a))
ans3 = np.einsum('ijij', np.einsum('ijkl->ikjl',a))
ans2 == ans3

>>> True

And these agree with the naive version up to the last decimal place

ans4 = 0.0
for i in xrange(3):
    for j in xrange(3):
        ans4 += a[i,i,j,j]
np.allclose(ans2, ans4) and np.allclose(ans3, ans4)

>>> True

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