Longest Ordered Subsequence

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence ( a1, a2, ..., aN) be any sequence ( ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8). 

Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

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Sample Input

7
1 7 3 5 9 4 8

Sample Output

4

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题目分析：从给定的序列中寻找出最长的升序子序列，并输出它的长度。可以用动态规划去写。 

#include<stdio.h>
#define maxn 10005

int d[maxn], a[maxn];

int main()
{
    int n, max_len;
    scanf("%d", &n);
    for(int i = 1; i <= n; i++)
       scanf("%d", &a[i]);

    // 递推 
    d[1] = 1;
    for(int i = 2; i <= n; i++) {
    	d[i] = 1;
    	for (int j = 1; j < i; j++) {
    		if (a[j] < a[i]) {
    			if (d[i] < d[j] + 1) {
    				d[i] = d[j] + 1;
				}
			}
		}
    }  
    max_len = 0;
    for(int i = 1; i <= n; i++)
        if(d[i] > max_len)
           max_len = d[i];
    printf("%d", max_len);
    return 0;  
}