Compressed Bracket Sequence

Description:

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.

Sample Input:

5
4 1 2 3 1

Sample Output:

5

Sample Input:

6
1 3 2 1 2 4

Sample Output:

6

Sample Input:

6
1 1 1 1 2 2

Sample Output:

7

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.