BORW - Black or White

It’s Black, It’s White, It’s Tough For You To Get By
Michael Jackson (1958-2009)


You have a sequence of integers. You can paint each of the integers black or white, or leave it unpainted. The black integers must appear in ascending order and the white integers must appear in descending order. The ascending/descending order must be strict, that is, two integers painted with the same color cannot be equal. Paint the sequence so as to minimize the number of unpainted integers.

Input

The input contains several test cases, each one described in exactly two lines. The first line contains an integer N indicating the number of elements in the sequence (1 ≤ N ≤ 200). The second line contains N integers Xi separated by single spaces, representing the sequence to paint (1 ≤ Xi ≤ 106 for 1 ≤ i ≤ N ). The last line of the input contains a single −1 and should not be processed as a test case.

Output

For each test case output a single line with an integer representing the minimum number of unpainted elements of the sequence, when the sequence is painted optimally following the rules described above.

Example

Input:
8
1 4 2 3 3 2 4 1
12
7 8 1 2 4 6 3 5 2 1 8 7
-1

Output:
0
2

Added by:Pablo Ariel Heiber
Date:2010-08-22
Time limit:9.584s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 VB.NET
Resource:FCEyN UBA ICPC Selection 2009

hide comments
2021-05-28 21:02:33
I think this is not a LIS/LDS problem. Normal DP problem with three states. Got AC in 2.62s
2021-05-04 10:31:58
@wk1948 come on side, need to talk XD
2020-11-15 14:21:54 Rafail Loizou
top down will work now worries
2020-10-10 14:27:32
AC in one go!
2020-09-13 21:53:06
getting TLE in python
2019-12-10 17:50:15
AC in 1 go !!
2019-09-28 12:47:08
I need more help on this. I constructed a backtracking solution but it's getting tle. Any hint how shuld I optimize it. My recursive function does not return therefore I am not able to do any memorization.
2019-07-11 13:56:29
what about Palindromic Pattern ?
2019-04-17 11:12:35
weak test cases
5
3 5 4 1 2
ans should be 1 but my accepted solution gives 0

Last edit: 2019-04-17 11:13:10
2019-03-17 19:14:07
AC in one Go => 1.91 s
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