A14383. Compressed Bracket Sequence

William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers $c_1, c_2, \dots, c_n$ 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) $[l, r]$ ( $l \le r$ ) 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.

The first line contains a single integer $n$ $(1 \le n \le 1000)$ , the size of the compressed sequence.

The second line contains a sequence of integers $c_1, c_2, \dots, c_n$ $(1 \le c_i \le 10^9)$ , the compressed sequence.

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.

In the first example a sequence (((()(()))( is described. This bracket sequence contains $5$ subsegments which form regular bracket sequences:

1. Subsequence from the $3$ rd to $10$ th character: (()(()))
2. Subsequence from the $4$ th to $5$ th character: ()
3. Subsequence from the $4$ th to $9$ th character: ()(())
4. Subsequence from the $6$ th to $9$ th character: (())
5. Subsequence from the $7$ th to $8$ th character: ()

In the second example a sequence ()))(()(()))) is described.

In the third example a sequence ()()(()) is described.