Solve the programming task below in a Python markdown code block.
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.


-----Input-----

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-----

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:

Subsequence from the $3$rd to $10$th character: (()(()))

Subsequence from the $4$th to $5$th character: ()

Subsequence from the $4$th to $9$th character: ()(())

Subsequence from the $6$th to $9$th character: (())

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.