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C. Compressed Bracket Sequence

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWilliam 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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