AtCoder Regular Contest 119 C

Posted 2021-05-27 Bcoi

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Problem Statement

There are $N$ buildings along the AtCoder Street, numbered $1$ through $N$ from west to east. Initially, Buildings $1, 2, \dots, N$ have the heights of $A_{1}, A_{2}, \dots, A_{N}$ , respectively.

Takahashi, the president of ARC Wrecker, Inc., plans to choose integers $l$ and $r$ $(1 \leq l < r \leq N)$ and make the heights of Buildings $l, l + 1, \dots, r$ all zero. To do so, he can use the following two kinds of operations any number of times in any order:

Set an integer $x$ $(l \leq x \leq r - 1)$ and increase the heights of Buildings $x$ and $x + 1$ by $1$ each.
Set an integer $x$ $(l \leq x \leq r - 1)$ and decrease the heights of Buildings $x$ and $x + 1$ by $1$ each. This operation can only be done when both of those buildings have heights of $1$ or greater.

Note that the range of $x$ depends on $(l, r)$ .

How many choices of $(l, r)$ are there where Takahashi can realize his plan?

Constraints

$2 \leq N \leq 300000$
$1 \leq A_{i} \leq 10^{9}$ $(1 \leq i \leq N)$
All values in input are integers.

Input

Input is given from Standard Input in the following format:

 $N$ 
 $A_{1}$   $A_{2}$   $\dots$   $A_{N}$

Output

Print the answer.

Sample Input 1 Copy

Copy

5
5 8 8 6 6

Sample Output 1 Copy

Copy

Takahashi can realize his plan for $(l, r) = (2, 3), (4, 5), (2, 5)$ .

For example, for $(l, r) = (2, 5)$ , the following sequence of operations make the heights of Buildings $2, 3, 4, 5$ all zero.

Decrease the heights of Buildings $4$ and $5$ by $1$ each, six times in a row.
Decrease the heights of Buildings $2$ and $3$ by $1$ each, eight times in a row.

For the remaining seven choices of $(l, r)$ , there is no sequence of operations that can realize his plan.

Sample Input 2 Copy

Copy

7
12 8 11 3 3 13 2

Sample Output 2 Copy

Copy

Takahashi can realize his plan for $(l, r) = (2, 4), (3, 7), (4, 5)$ .

For example, for html

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