C. Compressed Bracket Sequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output  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.InputThe 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.OutputOutput 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.ExamplesInput
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
NoteIn the first example a sequence (((()(()))( is described. This bracket sequence contains 5 subsegments which form regular bracket sequences:  Subsequence from the 3rd to 10th character: (()(()))  Subsequence from the 4th to 5th character: ()  Subsequence from the 4th to 9th character: ()(())  Subsequence from the 6th to 9th character: (())  Subsequence from the 7th to 8th character: () In the second example a sequence ()))(()(()))) is described.In the third example a sequence ()()(()) is described.
5
4 1 2 3 1

5 
['brute force', 'implementation', '*1800']