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: import sys
  input = sys.stdin.readline
  
  n = int(input())
  c = [0] + list(map(int, input().split()))
  c1, c2 = [0], [0]
  for i in range(1, n + 1):
      ci = c[i]
      if i % 2:
          c1.append(ci + c1[-1])
          c2.append(c2[-1])
      else:
          c2.append(ci + c2[-1])
          c1.append(c1[-1])
  dp = [[0] * (n + 1) for _ in range(n + 1)]
  ans = 0
  for x in range(1, n + 1, 2):
      for i in range(1, n + 1, 2):
          ci = c[i]
          if i + x > n:
              break
          j = i + x
          cj = c[j]
          if i == j - 1:
              m = min(ci, cj)
              ans += m
              dp[i][j] = 2 * m
          else:
              dp0 = dp[i + 2][j - 2]
              cnt1 = c1[j - 1] - c1[i] - dp0 // 2
              cnt2 = c2[j - 1] - c2[i] - dp0 // 2
              if cnt1 > cj or cnt2 > ci:
                  m = 0
                  dp[i][j] = dp0 + 2 * (min(cnt1, cj) + min(cnt2, ci))
              else:
                  m = min(ci - cnt2, cj - cnt1) + 1
                  ans += m
                  dp[i][j] = dp0 + 2 * (m + min(cnt1, cj) + min(cnt2, ci) - 1)
  print(ans)