An array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e.

A[0] + A[1] + ... + A[P1] = A[P+1] + ... + A[N2] + A[N1].

Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N1.

For example, consider the following array A consisting of N = 8 elements:

A[0] = -1

A[1] = 3

A[2] = -4

A[3] = 5

A[4] = 1

A[5] = -6

A[6] = 2

A[7] = 1

P = 1 is an equilibrium index of this array, because:

A[0] = 1 = A[2] + A[3] + A[4] + A[5] + A[6] + A[7]

P = 3 is an equilibrium index of this array, because:

A[0] + A[1] + A[2] = 2 = A[4] + A[5] + A[6] + A[7]

P = 7 is also an equilibrium index, because:

A[0] + A[1] + A[2] + A[3] + A[4] + A[5] + A[6] = 0

and there are no elements with indices greater than 7.

P = 8 is not an equilibrium index, because it does not fulfill the condition 0 P < N.

Write a function:

def solution(A)

that, given an array A consisting of N integers, returns any of its equilibrium indices. The function should return 1 if no equilibrium index exists.

For example, given array A shown above, the function may return 1, 3 or 7, as explained above.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [0..100,000];

each element of array A is an integer within the range [2,147,483,648..2,147,483,647].