Problem:
Maximum Sum Sequence

Given a sequence of numbers a1, a2, a3, ..., an, find the maximum sum of a contiguous subsequence of those numbers. Note that, a subsequence of one element is also a contiquous subsequence.

Input

The input consists of multiple datasets. Each data set consists of:

n
a1
a2
.
.
an

You can assume that 1 ≤ n ≤ 5000 and -100000 ≤ ai ≤ 100000.

The input end with a line consisting of a single 0.

Output

For each dataset, print the maximum sum in a line.

Sample Input

7
-5
-1
6
4
9
-6
-7
13
1
2
3
2
-2
-1
1
2
3
2
1
-2
1
3
1000
-200
201
0

Output for the Sample Input

19
14
1001

Solution in JAVA (judge verdict: Accepted)

import java.io.IOException;
import java.util.Scanner;

/**
 * using DP. O(N)
 * ????????????[x,i]????????§??¨?????????dp[i]??¨?????????(ai??§??????????????§??¨??????)
 * dp[0] = 0
 * dp[i] = max(dp[i-1] + ai, ai) -> ai??§??????????????§??¨?????? = a{i-1}??§??????????????§??¨?????? + ai, ai????????§???
 * ?±???????????????????max(dp[i])
 */
class Main {
	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);

		while(true) {
			int n = in.nextInt();
			if(n==0) break;

			int ans = Integer.MIN_VALUE;
			int dpi = 0;
			for (int i = 0; i < n; i++) {
				int ai = in.nextInt();
				dpi = Math.max(dpi + ai, ai);
				ans = Math.max(ans, dpi);
			}
			System.out.println(ans);
		}
	}
}