Problem D
Wavio Sequence 
Input: Standard Input

Output: Standard Output

Time Limit: 2 Seconds

Wavio is a sequence of integers. It has some interesting properties.

·  Wavio is of odd length i.e. L = 2*n + 1.

·  The first (n+1) integers of Wavio sequence makes a strictly increasing sequence.

·  The last (n+1) integers of Wavio sequence makes a strictly decreasing sequence.

·  No two adjacent integers are same in a Wavio sequence.

For example 1, 2, 3, 4, 5, 4, 3, 2, 0 is an Wavio sequence of length 9. But 1, 2, 3, 4, 5, 4, 3, 2, 2 is not a valid wavio sequence. In this problem, you will be given a sequence of integers. You have to find out the length of the longest Wavio sequence which is a subsequence of the given sequence. Consider, the given sequence as :

1 2 3 2 1 2 3 4 3 2 1 5 4 1 2 3 2 2 1.

Here the longest Wavio sequence is : 1 2 3 4 5 4 3 2 1. So, the output will be 9.

Input

The input file contains less than 75 test cases. The description of each test case is given below: Input is terminated by end of file.

Each set starts with a postive integer, N(1<=N<=10000). In next few lines there will be N integers.

Output

For each set of input print the length of longest wavio sequence in a line.

Sample Input  Output for Sample Input

10

1 2 3 4 5 4 3 2 1 10

19

1 2 3 2 1 2 3 4 3 2 1 5 4 1 2 3 2 2 1

5

1 2 3 4 5

9

9

1

#include <cstdio>
#include <algorithm>
using namespace std;
int LIS[10010];
int LDS[10010];
int minlis[10010];
int data[10010];
int binary(int l, int r , int x){int mid; while(l <= r){mid = (l + r) >> 1; if(minlis[mid] < x)  l = mid + 1; else  r = mid -1;}    return l;
}
int main(){int n, maxn, len;while(~scanf("%d", &n)){for(int i = 1; i <= n; i++)    scanf("%d", data + i);  minlis[1] = data[1]; LIS[1] = 1; len = 1;for(int i = 2; i <= n; i++){LIS[i] = binary(1, len, data[i]); minlis[LIS[i]] = data[i]; if(LIS[i] > len)  len++;}minlis[1] = data[n];  LDS[n] = 1; len = 1;for(int i = n-1; i > 0; i--){LDS[i] = binary(1, len, data[i]);   minlis[LDS[i]] = data[i];    if(LDS[i] > len)   len++;}maxn = 0;for(int i = 1; i <= n; i++)maxn = max(maxn , 2 * min(LIS[i] , LDS[i]) - 1);                   printf("%d\n", maxn);}return 0;
}

#include <cstdio>
#define max(a , b) ((a) > (b) ? (a) : (b))
int LIS[55];
int LDS[55];
long long minlis[55];
long long data[55];
int binary(int l, int r , int x){int mid; while(l <= r){mid = (l + r) >> 1;if(minlis[mid] < x)  l = mid + 1; else  r = mid -1;}    return l;
}
int main(){int n, maxn, len;while(~scanf("%d", &n) && n != 0){for(int i = 1; i <= n; i++)    scanf("%lld", data + i);  minlis[1] = data[1]; LIS[1] = 1; len = 1;for(int i = 2; i <= n; i++){LIS[i] = binary(1, len, data[i]); minlis[LIS[i]] = data[i]; if(LIS[i] > len)  len++;}minlis[1] = data[n];  LDS[n] = 1; len = 1;for(int i = n-1; i > 0; i--){LDS[i] = binary(1, len, data[i]);   minlis[LDS[i]] = data[i];    if(LDS[i] > len)   len++;}maxn = 0;for(int i = 1; i <= n; i++)maxn = max(maxn , LIS[i] + LDS[i] - 1);                   printf("%d\n", n - maxn);}return 0;
}