description: <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.
solution: #include <bits/stdc++.h>
  using namespace std;
  long long intersect_len(pair<long long, long long> A,
                          pair<long long, long long> B) {
    const auto &[la, ra] = A;
    const auto &[lb, rb] = B;
    if (ra < lb || rb < la) {
      return 0;
    }
    return min(ra, rb) - max(la, lb) + 1;
  }
  int main(void) {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);
    int n;
    cin >> n;
    vector<int> c(n + 1);
    for (int i = 0; i < (int)(n); i++) {
      cin >> c[i + 1];
    }
    long long res = 0;
    for (int l = 1; l <= n; l += 2) {
      long long mn = 0, tot = 0;
      for (int r = l + 1; r <= n; r += 2) {
        if (c[l] >= -mn) {
          res += intersect_len({max(1ll, -mn), c[l]}, {1 - tot, c[r] - tot});
        }
        tot -= c[r];
        mn = min(mn, tot);
        if (r + 1 <= n) {
          tot += c[r + 1];
        }
      }
    }
    cout << res << "\n";
    return 0;
  }
  