Count of Range Sum

Given an array of integers A and two integers B and C.
Find the number of range sums that lie in [ B, C ] inclusive.

Range sum S(i, j) is defined as the sum of the elements in A between indices i and j (i ≤ j), inclusive.

Input Format

The argument given is the integer array A and two integers B and C.

Output Format

 Find the number of range sums that lie in  [ B, C ] inclusive.

Constraints

1 <= length of the array <= 50000
-10^9 <= A[i] <= 10^9 

For Example

Input 1:
    A = [1, 2, 3]
    B = 4
    C = 6
Output 1:
    2
    Range Sum that lie between 4 and 6 are 6(1+2+3) and 5(2+3)

Input 2:
    A = [-5, 1, -2]
    B = -2
    C = 4
Output 2:
    3

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