Problem Description

Angel G-san and demon V-san attend a high school in the human world.
Today, they were assigned summer homework! The summer vacation lasts for $ N $ days, and the homework consists of $ N $ pages.
Demon V-san, being organized, decided to do one page of homework each day.
However, angel G-san, who is busy bringing blessings to the human world (under the guise of this), doesn't have time for homework!
Therefore, G-san decided to copy V-san's homework.

When G-san visits V-san on the $ i $-th day, V-san's mood is $ a_i $, and G-san can copy up to $ a_i $ pages of homework that day.
Since G-san is busy, she doesn't want to visit V-san more than necessary. How many times does G-san need to visit V-san minimally to complete the homework?

Note that when G-san visits V-san on the $ i $-th day, V-san will have already completed the $ i $-th page of homework.
Also, note that G-san cannot copy pages $ i+1 $ and beyond on the $ i $-th day.
Additionally, G-san cannot visit V-san more than once on the same day.

Input Format

The input is given from the standard input in the following format:

$ N $
$ a_1 $ $ a_2 $ $\ldots$ $ a_{N-1} $ $ a_N $

Output Format

Output the minimum number of times G-san needs to visit V-san to the standard output.

Sample Input and Output

Sample Input #1

5
1 3 2 2

Sample Output #1

2

Sample Input #2

6
1 2 1 1 2

Sample Output #2

4

Sample Input #3

8
1 2 1 2 3 1 3

Sample Output #3

3

Notes/Hints

Constraints

• All inputs are integers.
• $1\leq\ N\leq2\times10^5$
• $1\leq\ a_i\leq\ 10^9$

Sample Explanation 1

It is sufficient to visit on the 3rd and 5th days.

Sample Explanation 2

For example, it is sufficient to visit on the 1st, 3rd, 4th, and 6th days.

Sample Explanation 3

For example, it is sufficient to visit on the 3rd, 6th, and 8th days.

见题面 Input 部分

见题面 Output 部分