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

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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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