codeforces#P1556C. Compressed Bracket Sequence

Compressed Bracket Sequence

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 c1,c2,,cnc_1, c_2, \dots, c_n where cic_i 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].

You need to find the total number of continuous subsequences (subsegments) [l,r][l, r] (lrl \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.

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

The second line contains a sequence of integers c1,c2,,cnc_1, c_2, \dots, c_n (1ci109)(1 \le c_i \le 10^9), the compressed sequence.

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.

Input

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

The second line contains a sequence of integers c1,c2,,cnc_1, c_2, \dots, c_n (1ci109)(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.

Samples

输入数据 1

5
4 1 2 3 1

输出数据 1

5

输入数据 2

6
1 3 2 1 2 4

输出数据 2

6

输入数据 3

6
1 1 1 1 2 2

输出数据 3

7

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: ()

In the second example a sequence ()))(()(()))) is described.

In the third example a sequence ()()(()) is described.