human
PYTHON3 solution for "

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, ..., 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 ≤ 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 ≤ n ≤ 1000), the size of the compressed sequence.

The second line contains a sequence of integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 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:

  1. Subsequence from the 3rd to 10th character: (()(()))
  2. Subsequence from the 4th to 5th character: ()
  3. Subsequence from the 4th to 9th character: ()(())
  4. Subsequence from the 6th to 9th character: (())
  5. Subsequence from the 7th to 8th character: ()


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

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


 ... Give me a Python program to find the total number of continuous subsequences (subsegments) [l, r] (l ≤ r) of the original bracket sequence, which are regular bracket sequences?
assistant
#Here is Python program to find the total number of continuous subsequences (subsegments) [l, r] (l ≤ r) of the original bracket sequence, which are regular bracket sequences.
 def overlap(min1, max1, min2, max2):
    if max1 < min2 or max2 < min1:
        return 0
    return max(0, min(max1, max2) - max(min1, min2)) + 1

n = int(input())
arr = list(map(int, input().split()))
ans = 0
li = []
for i in range(0, n, 2):
    temp = 0
    a = 0
    b = arr[i] - 1
    temp += arr[i]
    flag = 0
    ans = 0
    for j in range(i + 1, n):
        c, d = 0, 0
        if j % 2 == 0:
            temp += arr[j]
        else:
            c = temp - 1
            d = temp - arr[j]
            temp -= arr[j]
            ans += overlap(a, b, d, c)
            b = min(b, temp)
        if temp < 0:
            break
    li.append(ans)
print(sum(li))