D. Array Painting
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of $$$n$$$ integers, where each integer is either $$$0$$$, $$$1$$$, or $$$2$$$. Initially, each element of the array is blue.

Your goal is to paint each element of the array red. In order to do so, you can perform operations of two types:

  • pay one coin to choose a blue element and paint it red;
  • choose a red element which is not equal to $$$0$$$ and a blue element adjacent to it, decrease the chosen red element by $$$1$$$, and paint the chosen blue element red.

What is the minimum number of coins you have to spend to achieve your goal?

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 2$$$).

Output

Print one integer — the minimum number of coins you have to spend in order to paint all elements red.

Examples
Input
3
0 2 0
Output
1
Input
4
0 0 1 1
Output
2
Input
7
0 1 0 0 1 0 2
Output
4
Note

In the first example, you can paint all elements red with having to spend only one coin as follows:

  1. paint the $$$2$$$-nd element red by spending one coin;
  2. decrease the $$$2$$$-nd element by $$$1$$$ and paint the $$$1$$$-st element red;
  3. decrease the $$$2$$$-nd element by $$$1$$$ and paint the $$$3$$$-rd element red.

In the second example, you can paint all elements red spending only two coins as follows:

  1. paint the $$$4$$$-th element red by spending one coin;
  2. decrease the $$$4$$$-th element by $$$1$$$ and paint the $$$3$$$-rd element red;
  3. paint the $$$1$$$-st element red by spending one coin;
  4. decrease the $$$3$$$-rd element by $$$1$$$ and paint the $$$2$$$-nd element red.