#include <bits/stdc++.h>
using namespace std;
const long long oo = 1e18;
const int N = 1e6;
long long n, m, x, y;
long long a[N], b[N], c[N], d[N], kq;
pair<long long, long long> t[N];
long long check(long long m) { return max((long long)0, m); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++)
    if (i % 2 == 1) {
      m = a[i];
      for (int j = i + 1; j <= n; j++) {
        if (j % 2 == 0)
          m = m - a[j];
        else
          m = m + a[j];
        if (j % 2 == 0)
          if (a[i] > m) {
            kq += a[i] - check(m);
            a[i] = m + 1;
          }
        if (m < 0) break;
      }
    }
  cout << kq;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

<image>

William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers c_1, c_2, ..., c_n where c_i is the number of consecutive brackets "(" if i is an odd number or the number of consecutive brackets ")" if i is an even number.

For example for a bracket sequence "((())()))" a corresponding sequence of numbers is [3, 2, 1, 3].

You need to find the total number of continuous subsequences (subsegments) [l, r] (l ≤ r) of the original bracket sequence, which are regular bracket sequences.

A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, sequences "(())()", "()" and "(()(()))" are regular, while ")(", "(()" and "(()))(" are not.

Input

The first line contains a single integer n (1 ≤ n ≤ 1000), the size of the compressed sequence.

The second line contains a sequence of integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 10^9), the compressed sequence.

Output

Output a single integer — the total number of subsegments of the original bracket sequence, which are regular bracket sequences.

It can be proved that the answer fits in the signed 64-bit integer data type.

Examples

Input


5
4 1 2 3 1


Output


5


Input


6
1 3 2 1 2 4


Output


6


Input


6
1 1 1 1 2 2


Output


7

Note

In the first example a sequence (((()(()))( is described. This bracket sequence contains 5 subsegments which form regular bracket sequences:

  1. Subsequence from the 3rd to 10th character: (()(()))
  2. Subsequence from the 4th to 5th character: ()
  3. Subsequence from the 4th to 9th character: ()(())
  4. Subsequence from the 6th to 9th character: (())
  5. Subsequence from the 7th to 8th character: ()



In the second example a sequence ()))(()(()))) is described.

In the third example a sequence ()()(()) is described.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long oo = 1e18;
const int N = 1e6;
long long n, m, x, y;
long long a[N], b[N], c[N], d[N], kq;
pair<long long, long long> t[N];
long long check(long long m) { return max((long long)0, m); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++)
    if (i % 2 == 1) {
      m = a[i];
      for (int j = i + 1; j <= n; j++) {
        if (j % 2 == 0)
          m = m - a[j];
        else
          m = m + a[j];
        if (j % 2 == 0)
          if (a[i] > m) {
            kq += a[i] - check(m);
            a[i] = m + 1;
          }
        if (m < 0) break;
      }
    }
  cout << kq;
  return 0;
}

```