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.":
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 process(A):
    n = len(A)
    answer = 0
    for i in range(0, n, 2):
        #a1 <= A[i]
        my_upper = A[i]
        my_lower = -1*float('inf')
        my_sum = 0
        for j in range(i+1, n):
            if j % 2==0:
                my_sum-=A[j]
            else:
                this_upper = min(my_upper, A[j]+my_sum)
                this_lower = max(1, my_lower)
                my_lower = max(my_lower, A[j]+my_sum)
                my_sum+=A[j]
                if this_upper >= this_lower:
                    answer+=(this_upper-this_lower+1)
                else:
                    answer+=0
    return answer
                

n = int(input())
A = [int(x) for x in input().split()]
print(process(A))