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;
  int32_t main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    {
      long long n;
      cin >> n;
      vector<long long> a(n + 1);
      for (long long i = 1; i <= n; ++i) {
        cin >> a[i];
        if (i % 2 == 0) a[i] *= -1;
      }
      vector<long long> pref(n + 1);
      for (long long i = 1; i <= n; ++i) pref[i] = pref[i - 1] + a[i];
      long long ans = 0;
      for (long long l = 1; l <= n; l += 2) {
        long long cur = 0;
        long long mn = a[l] - 1;
        for (long long r = l + 1; r <= n; r += 2) {
          cur += a[r - 1];
          if (cur + a[r] >= 0) {
            long long tt = cur + a[r];
            if (tt <= mn) {
              ans++;
              long long rem = mn - tt;
              ans += min(abs(a[r] + 1), rem);
            }
          } else {
            if (cur > 0) {
              long long tmp = -cur;
              long long tt = cur + tmp;
              if (tt <= mn) {
                ans++;
                long long rem = mn - tt;
                ans += min(abs(tmp + 1), rem);
              }
            }
          }
          cur += a[r];
          mn = min(mn, cur);
          if (mn < 0) break;
          ;
        }
      }
      cout << ans << '\n';
    }
    return 0;
  }
  