Palindromic Sum
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## Fast Fourier transform, Linear Algebra, Mathematics, Medium-Hard

Problem
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Given an array A of length N, find the number of non empty sub-arrays such that sum of all the elements in the sub-array is a palindrome. In other words, you have to find number of pairs $(i,\;j)$ such that $\sum_{x=i}^j A_x$ is a palindrome where $(1 \le i \le j \le N)$.

Input Format:
First line contains an integer, N $(1 \le N \le 5 * 10^5)$. Second line contains N space separated integers, $A_i$ $(1 \le A_i \le 2 * 10^6)$, elements of the array A. The sum of all the elements in the array is in the range $[1, 2 * 10^6]$.

Output Format:
Print an integer, number of non empty sub-arrays such that sum of all the elements in the sub-array is a palindrome.

SAMPLE INPUT
4
10 1 12 3


SAMPLE OUTPUT
3

Explanation

The 3 sub-arrays are $(10,\;1)$, 1 and 3.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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