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 PHP (judge verdict: Wrong Answer)

<?php

while (TRUE) {
    fscanf(STDIN, '%d', $n);
    if ($n === 0) {
        break;
    }
    $a = array();
    for ($i = 0; $i < $n; $i++) {
        fscanf(STDIN, '%d', $a[$i]);
    }
   
    $dp = array();
    $dp[0] = -1;
    for ($i = 1; $i <= $n; $i++) {
        $dp[$i] = $dp[$i - 1] >= 0 ? $dp[$i - 1] + $a[$i - 1] : $a[$i - 1];
    }
    $max = 0;
    for ($i = 0; $i <= $n; $i++) {
        if ($dp[$i] > $max) {
            $max = $dp[$i];
        }
    }

    echo $max;
    echo PHP_EOL;
}