MAXZERO

You are given a sequence of N integers ~A_1, A_2, ..., A_N~. Write a program to find the length of the longest continuous segment of this sequence, where the sum of the elements is zero.

Input

The first line of input contains a single natural number ~N~, the length of the sequence. The second line of input contains the ~N~ integers ~A_i~ of the sequence, separated in pairs by a single space.

Output

The output should consist of a single line containing exactly one natural number: the desired length of the longest continuous segment with a zero sum.

Constraints

~1 \le N \le 1.000.000~
~|A_i| \le 1.000~
Time Limit: 1 sec.
Maximum Available Memory: 64 MB

Example of Input - Output

1st

STDIN (maxzero.in)

16
25 -35 12 6 92 -115 17 2 2 2 -7 2 -9 16 2 -11

STDOUT (mazero.out)

6

Explanation of the first example: In the first example, the longest continuous segment of the sequence with a zero sum is ~92~, ~-115~, ~17~, ~2~, ~2~, ~2~, which has a length of ~6~.

2nd

STDIN (maxzero.in)

6
8 -12 3 7 -13 4

STDOUT (mazero.out)

0

Explanation of the second example: In the second example, there is no non-empty segment of the sequence with a zero sum.