Longest Subarray with Sum k

Given an array of integers, find the length of the longest contiguous subarray whose elements sum up to a given integer k. In other words, find the maximum length l such that for some indices i and j with j - i + 1 = l, the following holds:

$$\sum_{t=i}^{j} a_t = k$$

If no such subarray exists, output 0.

It is guaranteed that the input is provided via STDIN and the answer should be printed to STDOUT.

inputFormat

The first line contains an integer n (the number of elements in the array). The second line contains n space-separated integers, representing the array. The third line contains an integer k, the target sum.

Example:

5
1 -1 5 -2 3
3

outputFormat

Output a single integer representing the maximum length of a contiguous subarray that sums to k.

Example:

4

## sample

5
1 -1 5 -2 3
3

4