Perfect Subarray

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Arrays, Data Structures, Easy, One-dimensional, Prefix sum, prefix-sum

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Problem

You are given an array $A$ of $N$ integers. You need to count the subarrays which have the sum of all elements in it a perfect square.

Input
The first line contains an integer $N$ that denotes count of elements in the array. Next line contains $N$ space separated integers that denote elements of the array.

Output
In the output, you need to print the count of subarrays for which the sum of elements is a perfect square.

Constraints
$1 \le N \le 5000$
$1 \le A[i] \le 10^6$

Sample Input

4
1 4 2 3

Sample Output

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

The given array is: 1 4 2 3

Let us list the sum of all possible subarrays:

[1 , 1] = 1
[1 , 2] = 1 + 4 = 5
[1 , 3] = 1 + 4 + 2 = 7
[1 , 4] = 1 + 4 + 2 + 3 = 10
[2 , 2] = 4
[2 , 3] = 4 + 2 = 6
[2 , 4] = 4 + 2 + 3 = 9
[3 , 3] = 2
[3 , 4] = 2 + 3 = 5
[4 , 4] = 3

[1, 4, 9] = 3

Contributers:

Saurabh Joshi

Sanjay Gidwani