#include <bits/stdc++.h>
using namespace std;
long long max(int a, long long b) { return a > b ? a : b; }
long long max(long long a, int b) { return a > b ? a : b; }
void solve() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) cin >> v[i];
  long long ans = 0;
  for (long long i = 0; i < n; i += 2) {
    long long cd = 0;
    long long md = 0;
    for (long long j = i + 1; j < n; j += 2) {
      long long l = max(1, max(md, 1 - cd));
      long long r = min(v[i], v[j] - cd);
      ans += max(0, r - l + 1);
      cd -= v[j];
      md = max(md, -cd);
      if (j + 1 < n) cd += v[j + 1];
      md = max(md, -cd);
    }
  }
  cout << ans << endl;
}
signed main() {
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

<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;
long long max(int a, long long b) { return a > b ? a : b; }
long long max(long long a, int b) { return a > b ? a : b; }
void solve() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) cin >> v[i];
  long long ans = 0;
  for (long long i = 0; i < n; i += 2) {
    long long cd = 0;
    long long md = 0;
    for (long long j = i + 1; j < n; j += 2) {
      long long l = max(1, max(md, 1 - cd));
      long long r = min(v[i], v[j] - cd);
      ans += max(0, r - l + 1);
      cd -= v[j];
      md = max(md, -cd);
      if (j + 1 < n) cd += v[j + 1];
      md = max(md, -cd);
    }
  }
  cout << ans << endl;
}
signed main() {
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

```