CITY2 - A Famous City

After Mr. B arrived in Warsaw, he was shocked by the skyscrapers and took several photos. But now when he looks at these photos, he finds in surprise that he isn't even able to point out the number of buildings in it. So he decides to work it out as follows:

- divide the photo into n vertical pieces from left to right. The buildings in the photo can be treated as rectangles, the lower edge of which is the horizon. One building may span several consecutive pieces, but each piece can only contain one visible building, or no buildings at all.

- measure the height of each building in that piece.

- write a program to calculate the minimum number of buildings.

Mr. B has finished the first two steps, the remaining comes to you.

Input

Each test case starts with a line containing an integer n (1 <= n <= 100,000). Following this is a line containing n integers - the height of building in each piece respectively. Note that zero height means there are no buildings in this piece at all. All the input numbers will be nonnegative and less than 1,000,000,000.

Output

For each test case, display a single line containing the case number and the minimum possible number of buildings in the photo.

Example

Input:
3
1 2 3
3
1 2 1

Output:
Case 1: 3
Case 2: 2

Explanation

The possible configurations of the samples are illustrated below:


Added by:Fudan University Problem Setters
Date:2012-05-25
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:FDU Local Contest 2012

hide comments
2012-12-22 18:18:29 Swapnil R.Mehta
Take care of:-
5
0 1 0 1 0
ans->2
2012-12-15 18:15:09 nikoo28
the test cases by @Runtime Error helped me... :)
2012-11-29 15:38:21 Aditya Pande
@problemsetter
how does <snip> fail? i ve tried too many cases myself
submission id 8155135

please provide more test cases

even the good test cases given by RunTimeError didn't help me
finally accepted....

Last edit: 2022-08-30 20:35:48
2012-09-22 13:52:27 Sardar Khan
really easy :))
2012-08-31 13:17:35 (Tjandra Satria Gunawan)(曾毅昆)
easy problem :-)
For this problem, linear algo is faster than binary algo...
@Runtime Error: Thanks for the test cases ;-)
2012-07-08 08:04:04 rit
should it takes the first input as no of test cases?
what is the terminating criteria??
2012-07-03 01:26:50 praveen123
what is the point of having problem statement written in completely unclear way . You have not defined what is a building and what is overlapping of them , This should be given explicitly in problem statement . For me this problem looks like reading a language puzzle.


+1 To this comment ;)
+1 Too.

Last edit: 2012-11-01 01:16:18
2012-06-12 07:05:16 Runtime Error
more test cases
10
5 7 4 5 6 7 3 2 1 3
6
1 2 3 2 1 3
5
1 1 1 1 1
6
1 2 3 3 2 1
7
1 2 3 0 3 2 1

ans:
10
4
1
3
6

Last edit: 2012-06-12 07:13:05
2012-06-08 04:51:39 Nnavneetsinha
@Devil D Case 1: 5
2012-06-07 09:20:28 Devil D
whats the answer for
6
1 2 3 1 2 3
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