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.


For example, in a sequence &nbsp; <big><math>A</math></big>:

::::: &nbsp; <big><math>A_0 = -7</math></big>
::::: &nbsp; <big><math>A_1 =  1</math></big>
::::: &nbsp; <big><math>A_2 =  5</math></big>
::::: &nbsp; <big><math>A_3 =  2</math></big>
::::: &nbsp; <big><math>A_4 = -4</math></big>
::::: &nbsp; <big><math>A_5 =  3</math></big>
::::: &nbsp; <big><math>A_6 =  0</math></big>

3 &nbsp; is an equilibrium index, because:

::::: &nbsp; <big><math>A_0 + A_1 + A_2 = A_4 + A_5 + A_6</math></big>

6 &nbsp; is also an equilibrium index, because:

::::: &nbsp; <big><math>A_0 + A_1 + A_2 + A_3 + A_4 + A_5 = 0</math></big>

(sum of zero elements is zero)

7 &nbsp; is not an equilibrium index, because it is not a valid index of sequence <big><math>A</math></big>.


;Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).

Assume that the sequence may be very long.
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