<p>An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.</p>
<p>For example, in a sequence <big>$A$</big>:</p><p>:::: <big>$A_0 = -7$</big></p>
<p>:::: <big>$A_1 = 1$</big></p>
<p>:::: <big>$A_2 = 5$</big></p>
<p>:::: <big>$A_3 = 2$</big></p>
<p>:::: <big>$A_4 = -4$</big></p>
<p>:::: <big>$A_5 = 3$</big></p>
<p>:::: <big>$A_6 = 0$</big></p><p>3 is an equilibrium index, because:</p><p>:::: <big>$A_0 + A_1 + A_2 = A_4 + A_5 + A_6$</big></p><p>6 is also an equilibrium index, because:</p><p>:::: <big>$A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0$</big></p><p>(sum of zero elements is zero)</p><p>7 is not an equilibrium index, because it is not a valid index of sequence <big>$A$</big>.</p>
<p>Write a function that, given a sequence, returns its equilibrium indices (if any).</p><p>Assume that the sequence may be very long.</p>