#include <bits/stdc++.h>
using namespace std;
int CheckFail(vector<int> &arr, int begin, int end) {
  bool answer = true;
  while (begin < end) {
    answer &= arr[begin] == arr[end];
    if (!answer) {
      return begin;
    }
    ++begin;
    --end;
  }
  return begin;
}
bool CheckPalindrome(vector<int> &arr, int begin, int end) {
  return 2 * CheckFail(arr, begin, end) >= (begin + end);
}
int SolveProblem(const vector<int> &arr, int index) {
  size_t size = arr.size();
  vector<int> before(size), after(size);
  int middle = (size - 1) / 2;
  for (size_t i = index; i < size - index; ++i) {
    before[arr[i]] += 1;
  }
  int i;
  for (i = size - index - 1; i > middle; --i) {
    before[arr[i]] -= 1;
    after[arr[i]] += 1;
    if (before[arr[i]] < after[arr[i]]) {
      return i;
    }
  }
  while (arr[i] == arr[size - i - 1]) {
    int t = size - i - 1;
    if (i != t) {
      after[arr[t]] -= 1;
    }
    before[arr[i]] -= 1;
    if (before[arr[i]] < after[arr[i]]) {
      return i;
    }
    if (before[arr[t]] < after[arr[t]]) {
      return i;
    }
    --i;
  }
  return i;
}
int64_t GetAnswer(int64_t left, int64_t right, int64_t size) {
  return (left + 1) * (size - right);
}
int64_t Solve(vector<int> &arr, int index) {
  int64_t right = SolveProblem(arr, index);
  cerr << right << endl;
  return GetAnswer(index, right, arr.size());
}
bool CheckExistPalindrome(vector<int> &arr) {
  size_t size = arr.size();
  vector<int> m(size);
  for (size_t i = 0; i < size; ++i) {
    m[arr[i]] += 1;
  }
  int answer = 0;
  for (size_t i = 0; i < size; ++i) {
    answer += m[i] % 2;
  }
  return answer > 1;
}
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    --arr[i];
  }
  int64_t answer = 0;
  if (CheckPalindrome(arr, 0, arr.size() - 1)) {
    answer = arr.size();
    answer = answer * (answer - 1) / 2 + answer;
    cout << answer << endl;
    return 0;
  }
  if (CheckExistPalindrome(arr)) {
    cout << 0 << endl;
    return 0;
  }
  int64_t t = CheckFail(arr, 0, arr.size() - 1);
  answer -= GetAnswer(t, n - t - 1, n);
  answer += Solve(arr, t);
  reverse(arr.begin(), arr.end());
  answer += Solve(arr, t);
  cout << answer << endl;
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

Misha 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 ≤ 105).

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int CheckFail(vector<int> &arr, int begin, int end) {
  bool answer = true;
  while (begin < end) {
    answer &= arr[begin] == arr[end];
    if (!answer) {
      return begin;
    }
    ++begin;
    --end;
  }
  return begin;
}
bool CheckPalindrome(vector<int> &arr, int begin, int end) {
  return 2 * CheckFail(arr, begin, end) >= (begin + end);
}
int SolveProblem(const vector<int> &arr, int index) {
  size_t size = arr.size();
  vector<int> before(size), after(size);
  int middle = (size - 1) / 2;
  for (size_t i = index; i < size - index; ++i) {
    before[arr[i]] += 1;
  }
  int i;
  for (i = size - index - 1; i > middle; --i) {
    before[arr[i]] -= 1;
    after[arr[i]] += 1;
    if (before[arr[i]] < after[arr[i]]) {
      return i;
    }
  }
  while (arr[i] == arr[size - i - 1]) {
    int t = size - i - 1;
    if (i != t) {
      after[arr[t]] -= 1;
    }
    before[arr[i]] -= 1;
    if (before[arr[i]] < after[arr[i]]) {
      return i;
    }
    if (before[arr[t]] < after[arr[t]]) {
      return i;
    }
    --i;
  }
  return i;
}
int64_t GetAnswer(int64_t left, int64_t right, int64_t size) {
  return (left + 1) * (size - right);
}
int64_t Solve(vector<int> &arr, int index) {
  int64_t right = SolveProblem(arr, index);
  cerr << right << endl;
  return GetAnswer(index, right, arr.size());
}
bool CheckExistPalindrome(vector<int> &arr) {
  size_t size = arr.size();
  vector<int> m(size);
  for (size_t i = 0; i < size; ++i) {
    m[arr[i]] += 1;
  }
  int answer = 0;
  for (size_t i = 0; i < size; ++i) {
    answer += m[i] % 2;
  }
  return answer > 1;
}
int main() {
  int n;
  cin >> n;
  vector<int> arr(n);
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    --arr[i];
  }
  int64_t answer = 0;
  if (CheckPalindrome(arr, 0, arr.size() - 1)) {
    answer = arr.size();
    answer = answer * (answer - 1) / 2 + answer;
    cout << answer << endl;
    return 0;
  }
  if (CheckExistPalindrome(arr)) {
    cout << 0 << endl;
    return 0;
  }
  int64_t t = CheckFail(arr, 0, arr.size() - 1);
  answer -= GetAnswer(t, n - t - 1, n);
  answer += Solve(arr, t);
  reverse(arr.begin(), arr.end());
  answer += Solve(arr, t);
  cout << answer << endl;
  return 0;
}

```