human
PYTHON3 solution for "

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.":


 What is a Python program to find the total number of continuous subsequences (subsegments) [l, r] (l ≤ r) of the original bracket sequence, which are regular bracket sequences?
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#Here is Python program to find the total number of continuous subsequences (subsegments) [l, r] (l ≤ r) of the original bracket sequence, which are regular bracket sequences.
 def solve():
    n = int(input())
    sequence = [int(x) for x in input().split()]

    count = 0
    for start in range(0, n, 2):
        start_buffer = sequence[start]
        balance = 0
        for end in range(start + 1, n):
            if end % 2 == 0:
                balance += sequence[end]
            else:
                balance -= sequence[end]
                if balance <= 0 and end - start > 1:
                    count += 1
                if balance < 0:
                    if start_buffer + balance >= 0:
                        count += -balance
                        start_buffer += balance
                        balance = 0
                    else:
                        count += start_buffer
                        break
    print(count)

if __name__ == '__main__':
    solve()