There are \(n(1 \leq n \leq 1000000)\) books in the table, from left to right. Each book has a magic value \(a_i(-1000 \leq a_i \leq 1000, 1 \leq i \leq n)\),

 Please find the max length of a continuous  segment [l,r] , which satisfies \(\sum_{i=l}^r a_i > 0\).

The first line contains an integer \(n(1 \leq n \leq 1000000)\). The second line contains n integers, \(a_1,a_2...a_n\), each of them is between -1000 and 1000.

Print the max length of such segment.

In the sample, the longest postive segement is \([1,3]\)