Description:
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 Format:
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 Format:
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.
Note:
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.