#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
const long long MAXN = 2e5 + 100;
void solve() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  long long ans = 0;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i + 1 < n; i += 2) {
    long long bal = 0, mb = 0;
    for (int j = i + 1; j < n; j += 2) {
      long long r = min(a[j] - bal, a[i]);
      long long l = max(1LL, -mb);
      ans += max(0LL, r - l + 1);
      bal -= a[j];
      mb = min(mb, bal);
      if (j + 1 < n) bal += a[j + 1];
    }
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t = 1;
  while (t--) {
    solve();
    cout << '\n';
  }
}

### Prompt

Generate a cpp solution to 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;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
const long long MAXN = 2e5 + 100;
void solve() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  long long ans = 0;
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i + 1 < n; i += 2) {
    long long bal = 0, mb = 0;
    for (int j = i + 1; j < n; j += 2) {
      long long r = min(a[j] - bal, a[i]);
      long long l = max(1LL, -mb);
      ans += max(0LL, r - l + 1);
      bal -= a[j];
      mb = min(mb, bal);
      if (j + 1 < n) bal += a[j + 1];
    }
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t = 1;
  while (t--) {
    solve();
    cout << '\n';
  }
}

```