Equilibrium index

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 A:

A₀ = − 7

A₁ = 1

A₂ = 5

A₃ = 2

A₄ = − 4

A₅ = 3

A₆ = 0

so let start from A₀ where before there is no value then we  will take it as 0

ok and then

A₁ + A₂ + A₃ + A₄ + A₅+ A<sub>6   =1+5+2-4+3+0=8-4+3=7  

so 0 is not an equilibrium index 

next</sub>  A₁  position 

A₁ left side value is -7 and right side is 


A₂ +A₃ A₄ + A₅ + A<sub>6  

is
-6 so it is not equilibrium.    like that we need to check ....</sub>






3 is an equilibrium index, because:

A₀ + A₁ + A₂ = A₄ + A₅ + A₆

6 is also an equilibrium index, because:

A₀ + A₁ + A₂ + A₃ + A₄ + A₅ = 0

(sum of zero elements is zero)
7 is not an equilibrium index, because it is not a valid index of sequence A.
Write a function that, given a sequence, returns its equilibrium indices (if any). Assume that the sequence may be very long.