# William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers c1,c2,…,cnc1,c2,…,cn where cici is the number of consecutive brackets “(” if ii is an odd number or the number of consecutive brackets “)” if ii is an even number.- William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers c1,c2,…,cnc1,c2,…,cn where cici is the number of consecutive brackets “(” if ii is an odd number or the number of consecutive brackets “)” if ii is an even number.

## Compressed Bracket Sequence solution codeforces

William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers c1,c2,,cnc1,c2,…,cn where cici is the number of consecutive brackets “(” if ii is an odd number or the number of consecutive brackets “)” if ii is an even number.

For example for a bracket sequence “((())()))” a corresponding sequence of numbers is [3,2,1,3][3,2,1,3]. Compressed Bracket Sequence solution codeforces

You need to find the total number of continuous subsequences (subsegments) [l,r][l,r] (lrl≤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 Compressed Bracket Sequence solution codeforces

The first line contains a single integer nn (1n1000)(1≤n≤1000), the size of the compressed sequence.

The second line contains a sequence of integers c1,c2,,cnc1,c2,…,cn (1ci109)(1≤ci≤109), the compressed sequence.

Output Compressed Bracket Sequence solution codeforces

Output a single integer — the total number of subsegments of the original bracket sequence, which are regular bracket sequences.

It is guaranteed that the answer fits in the 64-bit integer data type.

Examples

input Compressed Bracket Sequence solution codeforces

Copy

6
1 3 2 1 2 4


input

Copy Compressed Bracket Sequence solution codeforces

6
1 1 1 1 2 2


Note

In the first example a sequence (((()(()))( is described. This bracket sequence contains 55 subsegments which form regular bracket sequences:

1. Subsequence from the 33rd to 1010th character: (()(()))
2. Subsequence from the 44th to 55th character: ()
3. Subsequence from the 44th to 99th character: ()(())
4. Subsequence from the 66th to 99th character: (())
5. Subsequence from the 77th to 88th character: ()

William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers c1,c2,…,cnc1,c2,…,cn where cici is the number of consecutive brackets “(” if ii is an odd number or the number of consecutive brackets “)” if ii is an even number.