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E. Misha and Palindrome Degree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMisha has an array of *n* integers indexed by integers from 1 to *n*. Let's define palindrome degree of array *a* as the number of such index pairs (*l*, *r*)(1 ≤ *l* ≤ *r* ≤ *n*), that the elements from the *l*-th to the *r*-th one inclusive can be rearranged in such a way that the whole array will be a palindrome. In other words, pair (*l*, *r*) should meet the condition that after some rearranging of numbers on positions from *l* to *r*, inclusive (it is allowed not to rearrange the numbers at all), for any 1 ≤ *i* ≤ *n* following condition holds: *a*[*i*] = *a*[*n* - *i* + 1].

Your task is to find the palindrome degree of Misha's array.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}).

The second line contains *n* positive integers *a*[*i*] (1 ≤ *a*[*i*] ≤ *n*), separated by spaces — the elements of Misha's array.

Output

In a single line print the answer to the problem.

Examples

Input

3

2 2 2

Output

6

Input

6

3 6 5 3 3 5

Output

0

Input

5

5 5 2 5 2

Output

4

Note

In the first sample test any possible pair (*l*, *r*) meets the condition.

In the third sample test following pairs (1, 3), (1, 4), (1, 5), (2, 5) meet the condition.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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